Ejercicio 272

Ejercicio 272

1. x 2 =5x x 2 –5x =0 x( x–5 ) =0 x 1 =0 x–5 =0 x 2 =5
2. 4 x 2 =–32x 4 x 2 +32x =0 4x( x+8 ) =0 4x =0 x 1 =0 x+8 =0 x 2 =–8
3. x 2 –3x =3 x 2 –4x x 2 –3 x 2 +4x–3x =0 –2 x 2 +x =0 x( –2x+1 ) =0 x 1 =0 –2x+1 =0 –2x =–1 x 2 = 1 2
4. 5 x 2 +4 =2( x+2 ) 5 x 2 + 4 =2x+ 4 5 x 2 –2x =0 x( 5x–2 ) =0 x 1 =0 5x–2 =0 5x =2 x 2 = 2 5
5. ( x–3 ) 2 – ( 2x+5 ) 2 =–16 x 2 –6x+9–( 4 x 2 +20x+25 ) =–16 x 2 –6x+9–4 x 2 –20x–25 =–16 –3 x 2 –26x– 16 = 16 3 x 2 +26x =0 x( 3x+26 ) =0 x 1 =0 3x+26 =0 3x =–26 x 2 =– 26 3
6. x 2 3 – x–9 6 = 3 2 Multiplicando la ecuación por 6 2 x 2 –x+ 9 = 9 x( 2x–1 ) =0 x 1 =0 2x–1 =0 2x =1 x 2 = 1 2
7. ( 4x–1 ) ( 2x+3 ) =( x+3 ) ( x–1 ) 8 x 2 +12x–2x– 3 = x 2 +2x– 3 8 x 2 +10x– x 2 –2x =0 7 x 2 +8x =0 x( 7x+8 ) =0 x 1 =0 7x+8 =0 7x =–8 x 2 =– 8 7
8. x+1 x–1 – x+4 x–2 =1 ( x+1 ) ( x–2 ) –( x+4 ) ( x–1 ) ( x–1 ) ( x–2 ) =1 x 2 –x–2–( x 2 +3x–4 ) =( x–1 ) ( x–2 ) x 2 –x–2– x 2 – 3x +4 = x 2 – 3x +2 0 = x 2 +x+ 2 – 2 0 =x( x+1 ) x 1 =0 0 =x+1 x 2 =–1