Ejercicio 265

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CAPITULO XXXIII

Ecuaciones de segundo grado
Ejercicio 265
Resolver las siguientes ecuaciones por la fórmula general:
x= b ± b 2 4ac 2a
  1. 3 x 2 5x+2 =0 x = 5 ± 5 2 4( 3 ) ( 2 ) 2( 3 ) x = 5 ± 2524 6 x = 5 ± 1 6 x 1 = 6 6 x 1 =1 x 2 = x 2 = 2 3
  2. 4 x 2 +3x22 =0 x = 3 ± 3 2 4( 4 ) (22 ) 2( 4 ) x = 3 ± 9352 8 x = 3 ± 361 8 x = 3 ± 19 8 x 1 = 8 x 1 =2 x 2 = x 2 = 11 4
  3. x 2 +11x =24 x 2 +11x+24 =0 x = 11 ± 1 1 2 4( 1 ) ( 24 ) 2( 1 ) x = 11 ± 12196 2 x = 11 ± 25 2 x = 11 ± 5 2 x 1 = 2 x 1 =8 x 2 = 2 x 2 =3
  4. x 2 =16x63 x 2 16x+63 =0 x = 16 ± 1 6 2 4( 1 ) ( 63 ) 2( 1 ) x = 16 ± 1 6 2 4( 1 ) ( 63 ) 2( 1 ) x = 16 ± 256252 2 x = 16 ± 4 2 x = 16 ± 2 2 x 1 = 2 x 1 =9 x 2 = 2 x 2 =7
  5. 12x49 x 2 =0 9 x 2 12x+4 =0 x = 12 ± 1 2 2 4( 9 ) ( 4 ) 2( 9 ) x = 12 ± 18 x = x = 2 3
  6. 5 x 2 7x90 =0 x = 7 ± 7 2 4( 5 ) (90 ) 2( 5 ) x = 7 ± 49+1800 10 x = 7 ± 1849 10 x = 7 ± 43 10 x 1 = 5 0 1 0 x 1 =5 x 2 = x 2 = 18 5
  7. 6 x 2 =x+222 6 x 2 x222 =0 x = 1 ± 14( 6 ) (222 ) 2( 6 ) x = 1 ± 1+5328 12 x = 1 ± 73 12 x 1 = x 1 = 37 6 x 2 = 12 x 2 =6
  8. x+11 =10 x 2 10 x 2 x11 =0 x = 1 ± 14( 10 ) (11 ) 2( 10 ) x = 1 ± 1+440 20 x = 1 ± 21 20 x 1 = x 1 = 11 10 x 2 = 20 20 x 2 =1
  9. 49 x 2 70x+25 =0 x = 70 ± 7 0 2 4( 49 ) ( 25 ) 2( 49 ) x = 70 ± 98 x = x = 5 7
  10. 12x7 x 2 +64 =0 7 x 2 12x64 =0 x = 12 ± 1 2 2 4( 7 ) (64 ) 2( 7 ) x = 12 ± 144+1792 14 x = 12 ± 1936 14 x = 12 ± 44 14 x 1 = 14 x 1 =4 x 2 = x 2 = 16 7
  11. x 2 =15x56 x 2 +15x+56 =0 x = 15 ± 1 5 2 4( 1 ) ( 56 ) 2( 1 ) x = 15 ± 225224 2 x = 15 ± 1 2 x 1 = 2 x 1 =7 x 2 = 2 x 2 =8
  12. 32 x 2 +18x17 =0 x = 18 ± 1 8 2 4( 32 ) (17 ) 2( 32 ) x = 18 ± 324+2176 64 x = 18 ± 2500 64 x = 18 ± 50 64 x 1 = 32 x 1 = 1 2 x 2 = x 2 = 17 16
  13. 176x =121+64 x 2 64 x 2 176x+121 =0 x = 176 ± 17 6 2 4( 64 ) ( 121 ) 2( 64 ) x = 176 ± 128 x = x = 11 8
  14. 8x+5 =36 x 2 36 x 2 8x5 =0 x = 8 ± 8 2 4( 36 ) (5 ) 2( 36 ) x = 8 ± 64+720 72 x = 8 ± 784 72 x = 8 ± 28 72 x 1 = 36 x 1 = 1 2 x 2 = x 2 = 5 18
  15. 27 x 2 +12x7 =0 x = 12 ± 1 2 2 4( 27 ) (7 ) 2( 27 ) x = 12 ± 144+756 54 x = 12 ± 900 54 x = 12 ± 30 54 x 1 = 18 x 1 = 1 3 x 2 = x 2 = 7 9
  16. 15x =25 x 2 +2 25 x 2 15x+2 =0 x = 15 ± 1 5 2 4( 25 ) ( 2 ) 2( 25 ) x = 15 ± 225200 50 x = 15 ± 25 50 x = 15 ± 5 50 x 1 = 2 0 5 0 x 1 = 2 5 x 2 = 1 0 5 0 x 2 = 1 5
  17. 8 x 2 2x3 =0 x = 2 ± 2 2 4( 8 ) (3 ) 2( 8 ) x = 2 ± 4+96 16 x = 2 ± 100 16 x = 2 ± 10 16 x 1 = x 1 = 3 4 x 2 = 8 x 2 = 1 2
  18. 105 =x+2 x 2 2 x 2 +x105 =0 x = 1 ± 14( 2 ) (105 ) 2( 2 ) x = 1 ± 14( 2 ) (105 ) 4 x = 1 ± 1+840 4 x = 1 ± 841 4 x = 1 ± 29 4 x 1 = 4 x 1 =7 x 2 = x 2 = 15 2