已知实数a满足a^2+4a-8=0,求1/a+1-a+3/a^2-1*a^2-2a+1/a^2+6a+9的值.
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已知实数a满足a^2+4a-8=0,求1/a+1-a+3/a^2-1*a^2-2a+1/a^2+6a+9的值.
已知实数a满足a^2+4a-8=0,求1/a+1-a+3/a^2-1*a^2-2a+1/a^2+6a+9的值.
已知实数a满足a^2+4a-8=0,求1/a+1-a+3/a^2-1*a^2-2a+1/a^2+6a+9的值.
1/(a+1)-(a+3)/(a^2-1)*(a^2-2a+1)/(a^2+6a+9)
=1/(a+1)-(a+3)/(a+1)(a-1)*(a-1)²/(a+3)²
=1/(a+1)-1/(a+1)(a+3)
=(a+2)/(a+1)(a+3)
=(a+2)/a²+4a+3
=正负2根号3/11
其中a^2+4a-8=0
所以a²+4a=8
(a+2)²-12=0
a+2=正负2根号3
解化简得。1/(a+1)-(a+3)/(a^2-1)*(a^2-2a+1)/(a^2+6a+9)
=1/(a+1)-(a+3)/(a+1)(a-1)*(a-1)²/(a+3)²
=1/(a+1)-(a-1)/(a+1)(a+3)
=a+3/(a+1)(a+3)-(a-1)/(a+1)(a+3)
=4/(a+1)(a+3)
∵a...
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解化简得。1/(a+1)-(a+3)/(a^2-1)*(a^2-2a+1)/(a^2+6a+9)
=1/(a+1)-(a+3)/(a+1)(a-1)*(a-1)²/(a+3)²
=1/(a+1)-(a-1)/(a+1)(a+3)
=a+3/(a+1)(a+3)-(a-1)/(a+1)(a+3)
=4/(a+1)(a+3)
∵a²+4a-8=0
∴(a+6)(a-2)=0 (ps。十字相乘。)
所以a+6=0 a=-6 或a-2=0 a=2
将-6或2代入4/(a+1)(a+3) 求值
正确答案 4/15
谢谢。。
收起
1/(a+1)-(a+3)/(a^2-1)*(a^2-2a+1)/(a^2+6a+9)
=1/(a+1)-(a+3)/(a+1)(a-1)*(a-1)²/(a+3)² ——这两部跟上个回答者的一样
=1/(a+1)-a-1/(a+1)(a+3)
=4/(a+1)(a+3)
=4/a^2+4a+3
因为a^2+4a-8=0
所以a^2+4a+3=11
所以4/a^2+4a+3(原式)=4/11
求采纳,谢谢!
a^2+4a-8=0
即(a+6)(a-2)=0
所以a=-6 或a=2
自己代数进去算