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Ejercicio 269

Gestor Baldor
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DESCARGA
CAPITULO XXXIII

Ecuaciones de segundo grado por descomposición en factores
Ejercicio 269
Resolver por descomposición en factores:
  1. x 2 –x–6 =0 ( x–3 ) ( x+2 ) =0 x–3 =0 x 1 =3 x+2 =0 x 2 =–2
  2. x 2 +7x =18 x 2 +7x–18 =0 ( x+9 ) ( x–2 ) =0 x+9 =0 x 1 =–9 x–2 =0 x 2 =2
  3. 8x–65 =– x 2 x 2 +8x–65 =0 ( x+13 ) ( x–5 ) =0 x+13 =0 x 1 =–13 x–5 =0 x 2 =5
  4. x 2 =108–3x x 2 +3x–108 =0 ( x+12 ) ( x–9 ) =0 x+12 =0 x 1 =–12 x–9 =0 x 2 =9
  5. 2 x 2 +7x–4 =0 2 x 2 –x+8x–4 =0 x( 2x–1 ) +4( 2x–1 ) =0 ( 2x–1 ) ( x+4 ) =0 x+4 =0 x 1 =–4 2x–1 =0 2x =1 x 2 = 1 2
  6. 6 x 2 =10–11x 6 x 2 +11x–10 =0 6 x 2 –4x+15x–10 =0 2x( 3x–2 ) +5( 3x–2 ) =0 ( 3x–2 ) ( 2x+5 ) =0 3x–2 =0 x 1 = 2 3 2x+5 =0 x 2 =– 5 2
  7. 20 x 2 –27x =14 20 x 2 –27x–14 =0 20 x 2 –35x+8x–14 =0 5x( 4x–7 ) +2( 4x–7 ) =0 ( 4x–7 ) ( 5x+2 ) =0 4x–7 =0 x 1 = 7 4 5x+2 =0 x 2 =– 2 5
  8. 7x =15–30 x 2 30 x 2 +7x–15 =0 30 x 2 –18x+25x–15 =0 6x( 5x–3 ) +5( 5x–3 ) =0 ( 5x–3 ) ( 6x+5 ) =0 6x+5 =0 x 1 =– 5 6 5x–3 =0 x 2 = 3 5
  9. 60 =8 x 2 +157x 8 x 2 +157x–60 =0 8 x 2 +160x–3x–60 =0 8x( x+20 ) –3( x+20 ) =0 ( x+20 ) ( 8x–3 ) =0 x+20 =0 x 1 =–20 8x–3 =0 x 2 = 3 8
  10. x( x–1 ) –5( x–2 ) =2 x 2 –x–5x+10–2 =0 x 2 –6x+8 =0 ( x–4 ) ( x–2 ) =0 x–4 =0 x 1 =4 x–2 =0 x 2 =2
  11. ( x–2 ) 2 – ( 2x+3 ) 2 =–80 [ ( x–2 ) +( 2x+3 ) ] [ ( x–2 ) –( 2x+3 ) ] =–80 [ x–2+2x+3 ] [ x–2–2x–3 ] =–80 ( 3x+1 ) ( –x–5 ) =–80 –3 x 2 –15x–x–5+80 =0 –3 x 2 –16x+75 =0 3 x 2 +16x–75 =0 3 x 2 –9x+25x–75 =0 3x( x–3 ) +25( x–3 ) =0 ( x–3 ) ( 3x+25 ) =0 x–3 =0 x 1 =3 3x+25 =0 x 2 =– 25 3
  12. 6 x 2 – 9 x =– 4 3 6–9x x 2 =– 4 3 3( 6–9x ) =–4 x 2 4 x 2 –27x+18 =0 4 x 2 –24x–3x+18 =0 4x( x–6 ) –3( x–6 ) =0 ( x–6 ) ( 4x–3 ) =0 x–6 =0 x 1 =6 4x–3 =0 x 2 = 3 4
  13. x+2 x +x = 74 x x+2+ x 2 x = 74 x x+2+ x 2 –74 =0 x 2 +x–72 =0 ( x+9 ) ( x–8 ) =0 x–8 =0 x 1 =8 x+9 =0 x 2 =–9
  14. ( x+2 ) 2 – 2x–5 3 =3 3 ( x+2 ) 2 –2x+5 3 =3 3( x 2 +4x+4 ) –2x+5 =9 3 x 2 +12x+12–2x+5–9 =0 3 x 2 +10x+8 =0 3 x 2 +6x+4x+8 =0 3x( x+2 ) +4( x+2 ) =0 ( x+2 ) ( 3x+4 ) =0 x+2 =0 x 1 =–2 3x+4 =0 x 2 =– 4 3
  15. x x–2 +x = 3x+15 4 x+x( x–2 ) x–2 = 3x+15 4 x+ x 2 –2x x–2 = 3x+15 4 x 2 –x x–2 = 3x+15 4 4( x 2 –x ) =( x–2 ) ( 3x+15 ) 4 x 2 –4x =3 x 2 +15x–6x–30 4 x 2 –4x–3 x 2 –9x+30 =0 x 2 –13x+30 =0 ( x–10 ) ( x–3 ) =0 x–10 =0 x 1 =10 x–3 =0 x 2 =3
  16. 6 x–4 – 4 x = 5 12 6x–4( x–4 ) x( x–4 ) = 5 12 6x–4x+16 x 2 –4x = 5 12 12( 2x+16 ) =5( x 2 –4x ) 24x+192 =5 x 2 –20x 0 =5 x 2 –20x–24x–192 5 x 2 –44x–192 =0 5 x 2 –60x+16x–192 =0 5x( x–12 ) +16( x–12 ) =0 ( x–12 ) ( 5x+16 ) =0 x–12 =0 x 1 =12 5x+16 =0 x 2 =– 16 5
  17. ( x–2 ) 3 – ( x–3 ) 3 =37 [ ( x–2 ) –( x–3 ) ] [ ( x–2 ) 2 +( x–2 ) ( x–3 ) + ( x–3 ) 2 ] =37 [ x 2 –4x+4+ x 2 –5x+6+ x 2 –6x+9 ] =37 3 x 2 –15x+19–37 =0 3 x 2 –15x–18 =0 Dividiendo la ecuación para 3 x 2 –5x–6 =0 ( x–6 ) ( x+1 ) =0 x–6 =0 x 1 =6 x+1 =0 x 2 =–1
  18. x–1 x+1 –2 = x+3 3 x–1–2( x+1 ) x+1 = x+3 3 x–1–2x–2 x+1 = x+3 3 –x–3 x+1 = x+3 3 3( –x–3 ) =( x+3 ) ( x+1 ) –3x–9 = x 2 +4x+3 –3x–9– x 2 –4x–3 =0 – x 2 –7x–12 =0 x 2 +7x+12 =0 ( x+4 ) ( x+3 ) =0 x+4 =0 x 1 =–4 x+3 =0 x 2 =–3
  19. 4x–1 2x+3 = 2x+1 6x+5 ( 4x–1 ) ( 6x+5 ) =( 2x+1 ) ( 2x+3 ) 24 x 2 +20x–6x–5 =4 x 2 +8x+3 24 x 2 +14x–5–4 x 2 –8x–3 =0 20 x 2 +6x–8 =0 Dividiendo la ecuación para 2 10 x 2 +3x–4 =0 10 x 2 –5x+8x–4 =0 5x( 2x–1 ) +4( 2x–1 ) =0 ( 2x–1 ) ( 5x+4 ) =0 2x–1 =0 x 1 = 1 2 5x+4 =0 x 2 =– 4 5
  20. 3x+2 4 =5– 9x+14 12x 3x+2 4 = 60x–9x–14 x 3x+2 = 51x–14 3x 3x( 3x+2 ) =51x–14 9 x 2 +6x–51x+14 =0 9 x 2 –45x+14 =0 9 x 2 –3x–42x+14 =0 3x( 3x–1 ) –14( 3x–1 ) =0 ( 3x–1 ) ( 3x–14 ) =0 3x–1 =0 x 1 = 1 3 3x–14 =0 x 2 = 14 3
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