(x^2-2)^2-14(x^2-2)+49

来源：学生作业帮助网编辑：作业帮时间：2024/12/02 08:59:20

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(x^2-2)^2-14(x^2-2)+49
(x^2-2)^2-14(x^2-2)+49

(x^2-2)^2-14(x^2-2)+49
分解因式吗?
原式=(x^2-2)^2-2*7*(x^2-2)+7^2
=[(x^2-2)-7]^2
=(x^2-9)^2
=(x^2-3^2)^2
=[(x+3)(x-3)]^2

(x^2-2)^2-14(x^2-2)+49
=(x^2-2-7)^2
=(x^2-9)^2
=[(x+3)(x-3)]^2
=(x+3)^2(x-3)^2

令x^2-2=a
则a²-14a+49=0
(a-7)²=0
a=±7
x²-2=7 x=±3
x²-2=-7 不成立
所以x=±3

解；原式=(x^2-2)^2-2×(x^2-2)×7+7^2
=(x^2-2-7)^2
=(x+3)^2(x-3)^2

(x^2-2)^2-14(x^2-2)+49
=(x^2-2-7)^2
=(x^2-9)^2
=(x-3)^2(x+3)^2
x1=3 x2=-3

(x^2-2)^2-14(x^2-2)+49
=[(x^2-2)-7]^2
=(x^2-9)^2
=(x-3)^2(x+3)^2
加油

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