CAPITULO XXXIII
Ecuaciones de segundo grado
Ecuaciones de segundo grado
- Ejercicio 267
Resolver las siguientes ecuaciones aplicando la fórmula particular:
x=–
m
2
±
m
2
4
–n
- x 2 –3x+2 =0 m=–3 n=2 x= 3 2 ± ( –3 ) 2 4 –2 x= 3 2 ± 9 4 –2 x= 3 2 ± 9–8 4 x= 3 2 ± 1 4 x= 3 2 ± 1 2 x 1 = 3 2 + 1 2 = 2 x 1 =2 x 2 = 3 2 – 1 2 = 2 2 x 2 =1
- x 2 –2x–15 =0 m=–2 n=–15 x= 2 2 ± ( –2 ) 2 4 –( –15 ) x=1 ± 4 4 +15 x=1 ± 1+15 x=1 ± 16 x=1 ± 4 x 1 =1+4 x 1 =5 x 2 =1–4 x 2 =–3
- x 2 =19x–88 x 2 –19x+88 =0 m=–19 n=88 x= 19 2 ± ( –19 ) 2 4 –88 x= 19 2 ± 361 4 –88 x= 19 2 ± 361–352 4 x= 19 2 ± 9 4 x= 19 2 ± 3 2 x 1 = 19 2 + 3 2 = 2 x 1 =11 x 2 = 19 2 – 3 2 = 2 x 2 =8
- x 2 +4x =285 x 2 +4x–285 =0 m=4 n=–285 x=– 2 ± 4 2 4 –( –285 ) x=–2 ± 4+285 x=–2 ± 289 x=–2 ± 17 x 1 =–2+17 x 1 =15 x 2 =–2–17 x 2 =–19
- 5x( x–1 ) –2( 2 x 2 –7x ) =–8 5 x 2 –5x–4 x 2 +14x+8 =0 x 2 +9x+8 =0 m=9 n=8 x=– 9 2 ± 9 2 4 –8 x=– 9 2 ± 81 4 –8 x=– 9 2 ± 81–32 4 x=– 9 2 ± 49 4 x=– 9 2 ± 7 2 x 1 =– 9 2 + 7 2 = –9+7 2 =– 2 2 x 1 =–1 x 2 =– 9 2 – 7 2 = –9–7 2 =– 2 x 2 =–8
- x 2 –( 7x+6 ) =x+59 x 2 –7x–6–x–59 =0 x 2 –8x–65 =0 m=–8 n=–65 x= 2 ± 8 2 4 –( –65 ) x=4 ± 4 +65 x=4 ± 16+65 x=4 ± 81 x=4 ± 9 x 1 =4+9 x 1 =13 x 2 =4–9 x 2 =–5
- ( x–1 ) 2 +11x+199 =3 x 2 – ( x–2 ) 2 x 2 –2x+1+11x+199 =3 x 2 –( x 2 –4x+4 ) x 2 +9x+200 =3 x 2 – x 2 +4x–4 x 2 +9x+200–2 x 2 –4x+4 =0 – x 2 +5x+204 =0 x 2 –5x–204 =0 m=–5 n=–204 x= 5 2 ± ( –5 ) 2 4 –( –204 ) x= 5 2 ± 25 4 +204 x= 5 2 ± 25+816 4 x= 5 2 ± 841 4 x= 5 2 ± 29 2 x 1 = 5 2 + 29 2 = 5+29 2 = 2 x 1 =17 x 2 = 5 2 – 29 2 = 5–29 2 =– 2 x 2 =–12
- ( x–2 ) ( x+2 ) –7( x–1 ) =21 x 2 –4–7x+7 =21 x 2 –7x+3–21 =0 x 2 –7x–18 =0 m=–7 n=–17 x= 7 2 ± ( –7 ) 2 4 –( –18 ) x= 7 2 ± 49 4 +18 x= 7 2 ± 49+72 4 x= 7 2 ± 121 4 x= 7 2 ± 11 2 x 1 = 7 2 + 11 2 = 7+11 2 = 2 x 1 =9 x 2 = 7 2 – 11 2 = 7–11 2 =– 2 x 2 =–2
- 2 x 2 –( x–2 ) ( x+5 ) =7( x+3 ) 2 x 2 –( x 2 +3x–10 ) =7x+21 2 x 2 – x 2 –3x+10–7x–21 =0 x 2 –10x–11 =0 m=–10 n=–11 x= 2 ± ( –10 ) 2 4 –( –11 ) x=5 ± 4 +11 x=5 ± 25+11 x=5 ± 36 x=5 ± 6 x 1 =5+6 x 1 =11 x 2 =5–6 x 2 =–1
- ( x–1 ) ( x+2 ) –( 2x–3 ) ( x+4 ) –x+14 =0 x 2 + x –2–( 2 x 2 +8x–3x–12 ) – x +14 =0 x 2 –2 x 2 –5x+12+12 =0 – x 2 –5x+24 =0 x 2 +5x–24 =0 m=5 n=–24 x=– 5 2 ± 5 2 4 –( –24 ) x=– 5 2 ± 25 4 +24 x=– 5 2 ± 25+96 4 x=– 5 2 ± 121 4 x=– 5 2 ± 11 2 x 1 =– 5 2 + 11 2 = –5+11 2 = 2 x 1 =3 x 2 =– 5 2 – 11 2 = –5–11 2 =– 2 x 2 =–8