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Ejercicio 284

Gestor Baldor
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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 ( x–2 ) ( 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 ± 4–16 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 ± 1–4 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 ± 9–36 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 = 3–3 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 ) ( x–2 ) =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 x–2 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 3x–16 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
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