下面两题怎么解(2+√30)/(√5+√6-√7)(x/x+1)+(x+1/x)=5/2
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![下面两题怎么解(2+√30)/(√5+√6-√7)(x/x+1)+(x+1/x)=5/2](/uploads/image/z/12974343-15-3.jpg?t=%E4%B8%8B%E9%9D%A2%E4%B8%A4%E9%A2%98%E6%80%8E%E4%B9%88%E8%A7%A3%282%2B%E2%88%9A30%29%2F%28%E2%88%9A5%2B%E2%88%9A6-%E2%88%9A7%29%28x%2Fx%2B1%29%2B%28x%2B1%2Fx%29%3D5%2F2)
下面两题怎么解(2+√30)/(√5+√6-√7)(x/x+1)+(x+1/x)=5/2
下面两题怎么解
(2+√30)/(√5+√6-√7)
(x/x+1)+(x+1/x)=5/2
下面两题怎么解(2+√30)/(√5+√6-√7)(x/x+1)+(x+1/x)=5/2
(2+√30)/(√5+√6-√7)
=(2+√30)(√5+√6+√7)/[(√5+√6)-√7][(√5+√6)+√7]
=(2+√30)(2√5+2√6+2√7+√150+√180+√210)/[(√5+√6)^2-(√7)^2]
=(2+√30)(2√5+2√6+2√7+5√6+6√5+√210)/[5+2√30+6-7]
=(2+√30)(8√5+7√6+2√7+√210)/(4+2√30)
=(2+√30)(8√5+7√6+2√7+√210)/2(2+√30)
=(8√5+7√6+2√7+√210)/2
令a=x/(x+1)
则(x+1)/x=1/a
所以a+1/a=5/2
a^2+1=5a/2
2a^2-5a+2=0
(2a-1)(a-2)=0
a=1/2,a=2
x/(x+1)=1/2
2x=x+1
x=1
x/(x+1)=2
x=2x+2
x=-2
分式方程要检验
经检验,x=1和x=-2是方程的解