分解因式:(x*x+4*x)(x*x+4*x+7)+12
回答 (2)
2007-03-03 11:49 am
✔ 最佳答案
(x^2+4x)(x^2+4x+7)+12=(x^2+4x)^2+7(x^2+4x)+12
=[(x^2+4x)+3][(x^2+4x)+4]
=(x^2+4x+3)(x^2+4x+4)
=(x+3)(x+1)(x+2)^2
2007-03-03 7:33 am
Let y=(x*x + 4*x)
(x*x+4*x)(x*x+4*x+7)+12
= y ( y + 7 ) +12
= y*y + 7*y +12
= (y+3) (y+4)
=> y = -3 or y = -4
=> x*x + 4*x = -3 or x*x+4*x = -4
=> x*x + 4*x +3=0 or x*x + 4*x + 4 =0
接下來用公式 [ -b +- sqrt(b^2-4ac) ] /2分別代入兩條算式找答案
(x*x+4*x)(x*x+4*x+7)+12
= y ( y + 7 ) +12
= y*y + 7*y +12
= (y+3) (y+4)
=> y = -3 or y = -4
=> x*x + 4*x = -3 or x*x+4*x = -4
=> x*x + 4*x +3=0 or x*x + 4*x + 4 =0
接下來用公式 [ -b +- sqrt(b^2-4ac) ] /2分別代入兩條算式找答案
參考: me
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