Ejercicio 285

CAPITULO XXXVI

Transformación de radicales dobles
Ejercicio 285
Transformar en suma algebraica de radicales simples:
  1. 5+ 24 Sea: a=5 b=24 m = a 2 b m = 5 2 24 m = 2524 m = 1 m =1 5+ 24 = a+m 2 + am 2 = 5+1 2 + 51 2 = 2 + 2 = 3 + 2
  2. 8 60 Sea: a=8 b=60 m = a 2 b m = 8 2 60 m = 6460 m = 4 m =2 8 60 = a+m 2 am 2 = 8+2 2 82 2 = 2 2 = 5 3
  3. 8+ 28 Sea: a=8 b=28 m = a 2 b m = 8 2 28 m = 6428 m = 36 m =6 8+ 28 = a+m 2 + am 2 = 8+6 2 + 86 2 = 2 + 2 2 = 7 +1
  4. 32 700 Sea: a=32 b=700 m = a 2 b m = 3 2 2 700 m = 1024700 m = 324 m =18 32 700 = a+m 2 am 2 = 32+18 2 3218 2 = 2 2 =5 7
  5. 14+ 132 Sea: a=14 b=132 m = a 2 b m = 1 4 2 132 m = 196132 m = 64 m =8 14+ 132 = a+m 2 + am 2 = 14+8 2 + 148 2 = 2 + 2 = 11 + 3
  6. 13+ 88 Sea: a=13 b=88 m = a 2 b m = 1 3 2 88 m = 16988 m = 81 m =9 13+ 88 = a+m 2 + am 2 = 13+9 2 + 139 2 = 2 + 2 = 11 + 2
  7. 11+2 30 = 11+ 120 Sea: a=11 b=120 m = a 2 b m = 1 1 2 120 m = 121120 m = 1 m =1 11+2 30 = a+m 2 + am 2 = 11+1 2 + 111 2 = 2 + 2 = 6 + 5
  8. 8418 3 = 84 972 Sea: a=84 b=972 m = a 2 b m = 8 4 2 972 m = 7056972 m = 6084 m =78 8418 3 = a+m 2 am 2 = 84+78 2 8478 2 = 2 2 =9 3
  9. 21+6 10 = 21+ 360 Sea: a=21 b=360 m = a 2 b m = 2 1 2 360 m = 441360 m = 81 m =9 21+6 10 = a+m 2 + am 2 = 21+9 2 + 219 2 = 2 + 2 = 15 + 6
  10. 28+14 3 = 28+ 588 Sea: a=28 b=588 m = a 2 b m = 2 8 2 588 m = 784588 m = 196 m =14 28+14 3 = a+m 2 + am 2 = 28+14 2 + 2814 2 = 2 + 2 = 21 + 7
  11. 144 6 = 14 96 Sea: a=14 b=96 m = a 2 b m = 1 4 2 96 m = 19696 m = 100 m =10 144 6 = a+m 2 am 2 = 14+10 2 1410 2 = 2 2 = 12 2 =2 3 2
  12. 55+30 2 = 55+ 1800 Sea: a=55 b=1800 m = a 2 b m = 5 5 2 1800 m = 30251800 m = 1225 m =35 55+30 2 = a+m 2 + am 2 = 55+35 2 + 5535 2 = 2 + 2 = 45 + 10 = 5. 3 2 + 10 =3 5 + 10
  13. 7312 35 = 73 5040 Sea: a=73 b=5040 m = a 2 b m = 7 3 2 5040 m = 53295040 m = 289 m =17 7312 35 = a+m 2 am 2 = 73+17 2 7317 2 = 2 2 = 45 28 = 5. 3 2 7. 2 2 =3 5 2 7
  14. 25360 7 = 253 25200 Sea: a=253 b=25200 m = a 2 b m = 25 3 2 25200 m = 6400925200 m = 38809 m =197 25360 7 = a+m 2 am 2 = 253+197 2 253197 2 = 2 2 =15 28 =15 7. 2 2 =152 7
  15. 29330 22 = 293 19800 Sea: a=293 b=19800 m = a 2 b m = 29 3 2 19800 m = 8584919800 m = 66049 m =257 29330 22 = a+m 2 am 2 = 293+257 2 293257 2 = 2 2 = 275 18 = 11. 5 2 2. 3 2 =5 11 3 2
  16. 5 6 + 2 3 Sea: a= 5 6 b= 2 3 m = a 2 b m = ( 5 6 ) 2 2 3 m = 25 36 2 3 m = 1 36 m = 1 6 5 6 + 2 3 = a+m 2 + am 2 = 5 6 + 1 6 2 + 5 6 1 6 2 = 1 2 + 4 2 = 1 2 + 1 3 = 1 2 2 2 + 1 3 3 3 = 2 2 + 3 3
  17. 3 4 1 2 Sea: a= 3 4 b= 1 2 m = a 2 b m = ( 3 4 ) 2 1 2 m = 9 16 1 2 m = 1 16 m = 1 4 3 4 1 2 = a+m 2 am 2 = 3 4 + 1 4 2 3 4 1 4 2 = 1 2 1 2 2 = 1 2 1 4 = 1 2 2 2 1 2 = 2 2 1 2 = 1 2 ( 2 1 )
  18. 9 16 + 1 8 Sea: a= 9 16 b= 1 8 m = a 2 b m = ( 9 16 ) 2 1 8 m = 81 256 1 8 m = 49 256 m = 7 16 9 16 + 1 8 = a+m 2 + am 2 = 9 16 + 7 16 2 + 9 16 7 16 2 = 1 2 + 1 8 2 = 1 2 + 1 16 = 1 2 2 2 + 1 4 = 2 2 + 1 4
    Hallar la raíz cuadrada de:
  19. 6+4 2 6+4 2 = 6+ 32 Sea: a=6 b=32 m = a 2 b m = 6 2 32 m = 3632 m = 4 m =2 6+4 2 = a+m 2 + am 2 = 6+2 2 + 62 2 = 2 + 2 =2+ 2
  20. 7+4 3 7+4 3 = 7+ 48 Sea: a=7 b=48 m = a 2 b m = 7 2 48 m = 4948 m = 1 m =1 7+4 3 = a+m 2 + am 2 = 7+1 2 + 71 2 = 2 + 2 =2+ 3
  21. 8+2 7 8+2 7 = 8+ 28 Sea: a=8 b=28 m = a 2 b m = 8 2 28 m = 6428 m = 36 m =6 8+2 7 = a+m 2 + am 2 = 8+6 2 + 86 2 = 2 + 2 2 = 7 +1
  22. 10+2 21 10+2 21 = 10+ 84 Sea: a=10 b=84 m = a 2 b m = 1 0 2 84 m = 10084 m = 16 m =4 10+2 21 = a+m 2 + am 2 = 10+4 2 + 104 2 = 2 + 2 = 7 + 3
  23. 18+6 5 18+6 5 = 18+ 180 Sea: a=18 b=180 m = a 2 b m = 1 8 2 180 m = 324180 m = 144 m =12 18+6 5 = a+m 2 + am 2 = 18+12 2 + 1812 2 = 2 + 2 = 15 + 3
  24. 242 143 242 143 = 24 572 Sea: a=24 b=572 m = a 2 b m = 2 4 2 572 m = 576572 m = 4 m =2 242 143 = a+m 2 am 2 = 24+2 2 242 2 = 2 2 = 13 11
  25. 3020 2 3020 2 = 30 800 Sea: a=30 b=800 m = a 2 b m = 3 0 2 800 m = 900800 m = 100 m =10 3020 2 = a+m 2 am 2 = 30+10 2 3010 2 = 2 2 = 20 10 = 5. 2 2 10 =2 5 10
  26. 9+6 2 9+6 2 = 9+ 72 Sea: a=9 b=72 m = a 2 b m = 9 2 72 m = 8172 m = 9 m =3 9+6 2 = a+m 2 + am 2 = 9+3 2 + 93 2 = 2 + 2 = 6 + 3
  27. 9824 5 9824 5 = 98 2880 Sea: a=98 b=2880 m = a 2 b m = 9 8 2 2880 m = 96042880 m = 6724 m =82 9824 5 = a+m 2 am 2 = 98+82 2 9882 2 = 2 2 = 90 8 = 10. 3 2 2. 2 2 =3 10 2 2

Ejercicio 284

CAPITULO XXXVI

ECUACIONES BINOMIAS Y TRINOMIAS
Ejercicio 284
Resolver las ecuaciones:
  1. x 6 7 x 3 8 =0 x 6 8 x 3 + x 3 8 =0 x 3 ( x 3 8 ) +( x 3 8 ) =0 ( x 3 8 ) ( x 3 +1 ) =0 (x2 ) ( x 2 +2x+4 ) (x+1 ) ( x 2 x+1 ) =0 x 1 2 =0 x 1 =2 x 2 +1 =0 x 2 =2 x 2 +2x+4 =0 x = 2 ± 2 2 4( 1 ) ( 4 ) 2( 1 ) x = 2 ± 416 2 x = 2 ± 12 2 x = 2 ± (1 ) ( 3 ) ( 2 2 ) 2 x = 2 ± 2 1 3 2 x = 2 (1 ± 3 i ) 2 x 3 =1+ 3 i x 4 =1 3 i x 2 x+1 =0 x = (1 ) ± (1 ) 2 4( 1 ) ( 1 ) 2( 1 ) x = 1 ± 14 2 x = 1 ± 1 3 2 x = 1 ± 3 i 2 x 5 = 1+ 3 i 2 x 6 = 1 3 i 2
  2. x 6 +30 x 3 +81 =0 x 6 +27 x 3 +3 x 3 +81 =0 x 3 ( x 3 +27 ) +3( x 3 +27 ) =0 ( x 3 +3 ) ( x 3 +27 ) =0 ( x 3 +3 ) (x+3 ) ( x 2 3x+9 ) =0 x 1 3 +3 =0 x 1 3 =3 x 1 = 3 3 x 1 = 33 x 2 +3 =0 x 2 =3 x 2 3x+9 =0 x = (3 ) ± (3 ) 2 4( 1 ) ( 9 ) 2( 1 ) x = 3 ± 936 2 x = 3 ± 27 2 x = 3 ± (1 ) ( 3 3 ) 2 x = 3 ± 3 3 1 2 x = 3 ± 3 3 i 2 x 3 = 33 3 i 2 x 4 = 3+3 3 i 2
  3. 8 x 6 +15 x 3 2 =0 8 x 6 +16 x 3 x 3 2 =0 8 x 3 ( x 2 +2 ) ( x 3 +2 ) =0 (8 x 3 1 ) ( x 3 +2 ) =0 8 x 1 3 1 =0 8 x 1 3 =1 x 1 3 = 1 8 x 1 = 1 8 x 1 = 1 2 x 2 3 +2 =0 x 2 3 =2 x 2 = 2 3 x 2 = 23
  4. x 8 41 x 4 +400 =0 x 8 16 x 4 25 x 4 +400 =0 x 4 ( x 4 16 ) 25( x 4 16 ) =0 ( x 4 25 ) ( x 4 16 ) =0 ( x 2 +5 ) ( x 2 5 ) ( x 2 4 ) ( x 2 +4 ) =0 ( x 2 +5 ) ( x 2 5 ) ( x 2 +4 ) (x+2 ) (x2 ) =0 x 1 +2 =0 x 1 =2 x 2 2 =0 x 2 =2 x 2 +5 =0 x 2 =5 x = ± 5 x 3 = 5 i x 4 = 5 i x 2 5 =0 x 2 =5 x = ± 5 x 5 = 5 x 6 = 5 x 2 +4 =0 x 2 =4 x = ± 4 x = ± (1 ) ( 2 2 ) x = ± 2 1 x = ± 2i x 7 =2i x 8 =2i
  5. x 10 33 x 5 +32 =0 x 10 x 5 32 x 5 +32 =0 x 5 ( x 2 1 ) 32( x 5 1 ) =0 ( x 5 32 ) ( x 5 1 ) =0 x 5 32 =0 x 5 =32 x 1 = 325 x 1 =2 x 5 1 =0 x 5 =1 x = 15 x 2 =1
  6. x 4 13 x 2 +36 =0 ( x 2 9 ) ( x 2 4 ) =0 x 2 9 =0 x 2 =9 1 x 2 =9 x 2 = 1 9 x = ± 1 9 x = ± 1 3 x 1 = 1 3 x 2 = 1 3 x 2 4 =0 x 2 =4 1 x 2 =4 x 2 = 1 4 x = ± 1 4 x = ± 1 2 x 3 = 1 2 x 4 = 1 2
  7. x 6 +35 x 3 =216 x 6 +35 x 3 +216 =0 x 6 +27 x 3 +8 x 3 +216 =0 x 3 ( x 3 +27 ) +8( x 3 +27 ) =0 ( x 3 +8 ) ( x 3 +27 ) =0 x 3 +8 =0 x 3 =8 1 x 3 =8 x 3 = 1 8 x 1 = 1 8 3 x 1 = 1 2 x 3 +27 =0 x 3 =27 1 x 3 =27 x 3 = 1 27 x 2 = 1 27 3 x 2 = 1 3
  8. x 10 =242 x 5 +243 x 10 242 x 5 243 =0 ( x 5 243 ) ( x 5 +1 ) =0 x 5 243 =0 x 5 =243 1 x 5 =243 x 5 = 1 243 x 1 = 1 243 5 x 1 = 1 3 x 5 +1 =0 x 5 =1 1 x 5 =1 x 5 =1 x 2 = 1 5 x 2 =1
  9. x 3 9 x 3 2 +8 =0 x 3 x 3 2 8 x 3 2 +8 =0 x 3 2 ( x 3 2 1 ) 8( x 3 2 1 ) =0 ( x 3 2 8 ) ( x 3 2 1 ) =0 x 3 2 8 =0 x 3 2 =8 ( x 3 2 ) 2 3 = 8 2 3 x 1 = 8 2 3 x 1 = 643 x 1 =4 x 3 2 1 =0 ( x 3 2 ) 2 3 = 1 2 3 x 2 =1
  10. x+ x 1 2 =6 x2 x 1 2 +3 x 1 2 6 =0 x 1 2 ( x 1 2 2 ) +3( x 1 2 2 ) =0 ( x 1 2 +3 ) ( x 1 2 2 ) =0 x 1 2 +3 =0 x 1 2 =3 ( x 1 2 ) 2 = (3 ) 2 x 1 =9 x 1 2 2 =0 x 1 2 =2 ( x 1 2 ) 2 = 2 2 x 2 =4
  11. 3x =16 x 5 3x16 x 1 2 +5 =0 3x x 1 2 15 x 1 2 +5 =0 x 1 2 (3 x 1 2 1 ) 5(3 x 1 2 1 ) =0 ( x 1 2 5 ) (3 x 1 2 1 ) =0 x 1 2 5 =0 x 1 2 =5 ( x 1 2 ) 2 = 5 2 x 1 =25 3 x 1 2 1 =0 3 x 1 2 =1 x 1 2 = 1 3 ( x 1 2 ) 2 = ( 1 3 ) 2 x = 1 9
  12. 2 x 1 2 5 x 1 4 +2 =0 2 x 1 2 x 1 4 4 x 1 4 +2 =0 x 1 4 (2 x 1 4 1 ) 2(2 x 1 4 1 ) =0 ( x 1 4 2 ) (2 x 1 4 1 ) =0 x 1 4 2 =0 x 1 4 =2 ( x 1 4 ) 4 = 2 4 x 1 =16 2 x 1 4 1 =0 2 x 1 4 =1 x 1 4 = 1 2 ( x 1 4 ) 4 = ( 1 2 ) 4 x 2 = 1 16

Ejercicio 283

CAPITULO XXXVI

ECUACIONES BINOMIAS Y TRINOMIAS
Ejercicio 283
Resolver las ecuaciones siguientes, hallando todas las raíces:
  1. x 4 10 x 2 +9 =0 ( x 2 9 ) ( x 2 1 ) =0 (x3 ) (x+3 ) (x1 ) (x+1 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 3 1 =0 x 3 =1 x 4 +1 =0 x 4 =1
  2. x 4 13 x 2 +36 =0 ( x 2 4 ) ( x 2 9 ) =0 (x2 ) (x+2 ) (x3 ) (x+3 ) =0 x 1 2 =0 x 1 =2 x 2 +2 =0 x 2 =2 x 3 3 =0 x 3 =3 x 4 +3 =0 x 4 =3
  3. x 4 29 x 2 +100 =0 ( x 2 25 ) ( x 2 4 ) =0 (x5 ) (x+5 ) (x2 ) (x+2 ) =0 x 1 5 =0 x 1 =5 x 2 +5 =0 x 2 =5 x 3 2 =0 x 3 =2 x 4 +2 =0 x 4 =2
  4. x 4 61 x 2 +900 =0 ( x 2 36 ) ( x 2 25 ) =0 (x6 ) (x+6 ) (x5 ) (x+5 ) =0 x 1 6 =0 x 1 =6 x 2 +6 =0 x 2 =6 x 3 5 =0 x 3 =5 x 4 +5 =0 x 4 =5
  5. x 4 +3 x 2 4 =0 ( x 2 +4 ) ( x 2 1 ) =0 ( x 2 +4 ) (x1 ) (x+1 ) =0 x 1 1 =0 x 1 =1 x 2 +1 =0 x 2 =1 x 2 +4 =0 x 2 =4 x = ± (1 ) ( 2 ) 2 x = ± 2 1 x = ± 2i x 3 =2i x 4 =2i
  6. x 4 +16 x 2 225 =0 ( x 2 +25 ) ( x 2 9 ) =0 ( x 2 +25 ) (x3 ) (x+3 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 2 +25 =0 x 2 =25 x = ± (1 ) ( 5 2 ) x = ± 5 1 x = ± 5i x 3 =5i x 4 =5i
  7. x 4 45 x 2 196 =0 ( x 2 49 ) ( x 2 +4 ) =0 (x7 ) (x+7 ) ( x 2 +4 ) =0 x 1 7 =0 x 1 =7 x 2 +7 =0 x 2 =7 x 2 +4 =0 x 2 =4 x = ± 2 2 x = ± 2 1 x = ± 2i x 3 =2i x 4 =2i
  8. x 4 6 x 2 +5 =0 ( x 2 5 ) ( x 2 1 ) =0 ( x 2 5 ) (x1 ) (x+1 ) =0 x 1 1 =0 x 1 =1 x 2 +1 =0 x 2 =1 x 2 5 =0 x = ± 5 x 3 = 5 x 4 = 5
  9. 4 x 4 37 x 2 +9 =0 4 x 4 x 2 36 x 2 +9 =0 x 2 (4 x 2 1 ) 9(4 x 2 1 ) =0 ( x 2 9 ) (4 x 2 1 ) =0 (x3 ) (x+3 ) (4 x 2 1 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 4 x 2 1 =0 4 x 2 =1 x 2 = 1 4 x = ± 1 4 x = ± 1 2 1 x 3 = 1 2 1 x 4 = 1 2 1
  10. 9 x 4 40 x 2 +16 =0 9 x 4 36 x 2 4 x 2 +16 =0 9 x 2 ( x 2 4 ) 4( x 2 4 ) =0 (9 x 2 4 ) ( x 2 4 ) =0 (9 x 2 4 ) (x2 ) (x+2 ) =0 x 1 2 =0 x 1 =2 x 2 +2 =0 x 2 =2 9 x 2 4 =0 9 x 2 =4 x 2 = 4 9 x = ± 4 9 x = ± 2 3 x 3 = 2 3 x 4 = 2 3
  11. 25 x 4 +9 x 2 16 =0 25 x 4 +25 x 2 16 x 2 16 =0 25 x 2 ( x 2 +1 ) 16( x 2 +1 ) =0 (25 x 2 16 ) ( x 2 +1 ) =0 x 2 +1 =0 x 2 =1 x = ± 1 x 1 =i x 2 =i 25 x 2 16 =0 25 x 2 =16 x 2 = 16 25 x = ± 16 25 x = ± 4 5 x 3 = 4 5 x 4 = 4 5
  12. 4 x 4 +11 x 2 3 =0 4 x 4 x 2 +12 x 2 3 =0 x 2 (4 x 2 1 ) +3(4 x 2 1 ) =0 ( x 2 +3 ) (4 x 2 1 ) =0 4 x 2 1 =0 4 x 2 =1 x 2 = 1 4 x = ± 1 4 x = ± 1 2 x 1 = 1 2 x 2 = 1 2 x 2 +3 =0 x 2 =3 x = ± 3 x = ± 1 3 x = ± 3 i x 3 = 3 i x 4 = 3 i
  13. (2 x 2 +1 ) 2 ( x 2 3 ) 2 =80 [(2 x 2 +1 ) ( x 2 3 ) ] [(2 x 2 +1 ) +( x 2 3 ) ] =80 [2 x 2 +1 x 2 +3 ] [2 x 2 +1+ x 2 3 ] =80 ( x 2 +4 ) (3 x 2 2 ) =80 3 x 4 2 x 2 +12 x 2 8 =80 3 x 4 +10 x 2 88 =0 3 x 4 12 x 2 +22 x 2 88 =0 3 x 2 ( x 2 4 ) +22( x 2 4 ) =0 (3 x 2 +22 ) ( x 2 4 ) =0 x 2 4 =0 x = ± 4 x = ± 2 x 1 =2 x 2 =2 3 x 2 +22 =0 3 x 2 =22 x 2 = 22 3 x = ± 22 3 x = ± (1 ) ( 22 3 ) x = ± 22 3 i x 3 = 22 3 i x 4 = 22 3 i
  14. x 2 (3 x 2 +2 ) =4( x 2 3 ) +13 3 x 4 +2 x 2 =4 x 2 12+13 3 x 4 +2 x 2 4 x 2 1 =0 3 x 4 2 x 2 1 =0 3 x 4 3 x 2 + x 2 1 =0 3 x 2 ( x 2 1 ) +( x 2 1 ) =0 (3 x 2 +1 ) ( x 2 1 ) =0 x 2 1 =0 x 2 =1 x = ± 1 x = ± 1 x 1 =1 x 2 =1 3 x 2 +1 =0 3 x 2 =1 x 2 = 1 3 x = ± 1 3 x = ± (1 ) ( 1 3 ) x = ± 1 3 i x 3 = 1 3 i x 4 = 1 3 i

Ejercicio 282

CAPITULO XXXVI

ECUACIONES BINOMIAS Y TRINOMIAS
Ejercicio 282
Resolver las ecuaciones:
  1. x 4 1 =0 ( x 2 +1 ) ( x 2 1 ) =0 ( x 2 +1 ) (x+1 ) (x1 ) =0 x 1 +1 =0 x 1 =1 x 2 1 =0 x 2 =1 x 2 +1 =0 x 2 =1 x = ± 1 x 3 =i x 4 =i
  2. x 3 +1 =0 (x+1 ) ( x 2 x+1 ) =0 x+1 =0 x 1 =1 x 2 x+1 =0 x = (1 ) ± (1 ) 2 4( 1 ) ( 1 ) 2( 1 ) x = 1 ± 14 2 x = 1 ± 1 3 2 x = 1 ± 3 i 2 x 1 = 1+ 3 i 2 x 2 = 1 3 i 2
  3. x 4 =81 x 4 81 =0 ( x 2 +9 ) ( x 2 9 ) =0 ( x 2 +9 ) (x3 ) (x+3 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 2 +9 =0 x 2 =9 x = ± 3 2 x = ± 3 1 x 3 =3i x 4 =3i
  4. x 4 256 =0 ( x 2 +16 ) ( x 2 16 ) =0 ( x 2 +16 ) (x4 ) (x+4 ) =0 x 1 4 =0 x 1 =4 x 2 +4 =0 x 2 =4 x 2 +16 =0 x 2 =16 x = ± 4 2 x = ± 4 1 x 3 =4i x 4 =4i
  5. x 3 +8 =0 (x+2 ) ( x 2 2x+4 ) =0 x 1 +2 =0 x 1 =2 x 2 2x+4 =0 x = (2 ) ± (2 ) 2 4( 1 ) ( 4 ) 2( 1 ) x = 2 ± 416 2 x = 2 ± 12 2 x = 2 ± (3 ) ( 2 2 ) 2 x = 2 ± 2 ( 3 ) (1 ) 2 x = 2 (1 ± 3 i ) 2 x 2 =1+ 3 i x 3 =1 3 i
  6. x 4 625 =0 ( x 2 +25 ) ( x 2 25 ) =0 ( x 2 +25 ) (x5 ) (x+5 ) =0 x 1 5 =0 x 1 =5 x 2 +5 =0 x 2 =5 x 2 +25 =0 x 2 =25 x = ± 25 x = ± (1 ) ( 5 2 ) x = ± 5i x 3 =5i x 4 =5i
  7. x 3 +64 =0 (x+4 ) ( x 2 4x+16 ) =0 x+4 =0 x 1 +4 =0 x 1 =4 x 2 4x+16 =0 x = (4 ) ± (4 ) 2 4( 1 ) ( 16 ) 2( 1 ) x = 4 ± 1664 2 x = 4 ± 48 2 x = 4 ± (3 ) ( 4 2 ) 2 x = 4 ± 4 3 1 2 x = 2 (2 ± 2 3 i ) 2 x 2 =2+2 3 i x 3 =22 3 i
  8. x 6 729 =0 ( x 3 27 ) ( x 3 +27 ) =0 (x3 ) ( x 2 +3x+9 ) (x+3 ) ( x 2 3x+9 ) =0 x 1 3 =0 x 1 =3 x 2 +3 =0 x 2 =3 x 2 +3x+9 =0 x = 3 ± 3 2 4( 1 ) ( 9 ) 2( 1 ) x = 3 ± 936 2 x = 3 ± 27 2 x = 3 ± (1 ) ( 3 3 ) 2 x = 3 ± 3 3 1 2 x = 3 ± 3 3 i 2 x 3 = 33 3 i 2 x 4 = 3+3 3 i 2 x 2 3x+9 =0 x = (3 ) ± (3 ) 2 4( 1 ) ( 9 ) 2( 1 ) x = 3 ± 936 2 x = 3 ± 27 2 x = 3 ± (1 ) ( 3 3 ) 2 x = 3 ± 3 3 1 2 x = 3 ± 3 3 i 2 x 5 = 33 3 i 2 x 6 = 3+3 3 i 2
  9. Hallar las raíces cúbicas de 8.
    x 3 =8 x 3 8 =0 (x2 ) ( x 2 +2x+4 ) =0 x 1 2 =0 x 1 =2 x 2 +2x+4 =0 x = 2 ± 2 2 4( 1 ) ( 4 ) 2( 1 ) x = 2 ± 416 2 x = 2 ± 12 2 x = 2 ± (1 ) ( 3 ) ( 2 2 ) 2 x = 2 ± 2 1 3 2 x = 2 (1 ± 3 i ) 2 x 2 =1+ 3 i x 3 =1 3 i
  10. Hallar las raíces cuartas de 64.
    x 4 =64 x 4 64 =0 ( x 2 +8 ) ( x 2 8 ) =0 x 2 8 =0 x 2 =8 x = ± 8 x = ± 2 3 x = ± 2 2 x 1 =2 2 x 2 =2 2 x 2 +8 =0 x 2 =8 x = ± 8 x = ± 2 3 x = ± 2 2 1 x 1 =2 2 i x 2 =2 2 i