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CAPITULO XXXIII

Ecuaciones incompletas de segundo grado
Ejercicio 271
Resolver las ecuaciones:
  1. 3 x 2 =48 x 2 = 3 x = 16 x = ± 4
  2. 5 x 2 9 =46 5 x 2 =46+9 5 x 2 =55 x 2 = 5 x = ± 11
  3. 7 x 2 +14 =0 7( x 2 +2 ) =0 x 2 +2 =0 x 2 =2 x = 2 x = ± 2 i
  4. 9 x 2 a 2 =0 (3x+a ) (3xa ) =0 3x+a =0 3x =a x 1 = a 3 3xa =0 3x =a x 2 = a 3
  5. (x+5 ) (x5 ) =7 x 2 25 =7 x 2 =257 x 2 =18 x = 18 x = 3 2 .2 x = ± 3 2
  6. (2x3 ) (2x+3 ) 135 =0 4 x 2 9135 =0 4 x 2 =144 x 2 = 4 x = 36 x = ± 6
  7. 3(x+2 ) (x2 ) = (x4 ) 2 +8x 3( x 2 4 ) = x 2 8x +16+ 8x 3 x 2 12 = x 2 +16 3 x 2 x 2 =16+12 2 x 2 =28 x 2 = 2 x = ± 14
  8. (x+ 1 3 ) (x 1 3 ) = 1 3 x 2 1 9 = 1 3 x 2 = 1 3 + 1 9 x 2 = 3+1 9 x 2 = 4 9 x = 4 9 x = ± 2 3
  9. (2x1 ) (x+2 ) (x+4 ) (x1 ) +5 =0 2 x 2 +4xx2( x 2 +3x4 ) +5 =0 2 x 2 + 3x 2 x 2 3x +4+5 =0 x 2 +7 =0 x 2 =7 x = 7 x = ± 7 i
  10. 5 2 x 2 1 6 x 2 = 7 12 151 6 x 2 = 7 2 = 7 x 2 x = 4 x = ± 2
  11. 2x3 x3 = x2 x1 (2x3 ) (x1 ) =(x2 ) (x3 ) 2 x 2 2x 3x +3 = x 2 5x +6 2 x 2 x 2 =63 x 2 =3 x = ± 3
  12. x 2 5 3 + 4 x 2 1 5 14 x 2 1 15 =0 Multiplicando la ecuación por 15 5( x 2 5 ) +3(4 x 2 1 ) 14 x 2 +1 =0 5 x 2 25+12 x 2 314 x 2 +1 =0 3 x 2 27 =0 3( x 2 9 ) =0 x 2 9 =0 x 2 =9 x = 9 x = ± 3
  13. 2x3 x 2 +1 x2 =7 (2x3 ) (x2 ) x 2 1 x2 =7 2 x 2 4x3x+6 x 2 1 =7(x2 ) x 2 7x +5 = 7x +14 x 2 =5+14 x 2 =9 x = 9 x = ± 3
  14. 3 3 4 x 2 1 =2 3 4 x 2 1 =23 3 4 x 2 1 =1 3 =4 x 2 1 0 =4 x 2 13 4 x 2 4 =0 4( x 2 1 ) =0 x 2 1 =0 (x1 ) (x+1 ) =0 x1 =0 x 1 =1 x+1 =0 x 2 =1
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