Ejercicio 271

Ejercicio 271

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 ) ( 3x–a ) =0 3x+a =0 3x =–a x 1 =– a 3 3x–a =0 3x =a x 2 = a 3
5. ( x+5 ) ( x–5 ) =–7 x 2 –25 =–7 x 2 =25–7 x 2 =18 x = 18 x = 3 2 .2 x = ± 3 2
6. ( 2x–3 ) ( 2x+3 ) –135 =0 4 x 2 –9–135 =0 4 x 2 =144 x 2 = 4 x = 36 x = ± 6
7. 3( x+2 ) ( x–2 ) = ( x–4 ) 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. ( 2x–1 ) ( x+2 ) –( x+4 ) ( x–1 ) +5 =0 2 x 2 +4x–x–2–( x 2 +3x–4 ) +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 15–1 6 x 2 = 7 2 = 7 x 2 x = 4 x = ± 2
11. 2x–3 x–3 = x–2 x–1 ( 2x–3 ) ( x–1 ) =( x–2 ) ( x–3 ) 2 x 2 – 2x – 3x +3 = x 2 – 5x +6 2 x 2 – x 2 =6–3 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 –3–14 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. 2x–3– x 2 +1 x–2 =–7 ( 2x–3 ) ( x–2 ) – x 2 –1 x–2 =–7 2 x 2 –4x–3x+6– x 2 –1 =–7( x–2 ) 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 =2–3 3 4 x 2 –1 =1 3 =4 x 2 –1 0 =4 x 2 –1–3 4 x 2 –4 =0 4( x 2 –1 ) =0 x 2 –1 =0 ( x–1 ) ( x+1 ) =0 x–1 =0 x 1 =1 x+1 =0 x 2 =–1