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Question

Solve:
xx+1+x+1x=52

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Solution

Given xx+1+x+1x=52
x2+(x+1)2x(x+1)=52
4x2+4x+2=5x2+5x
x2+x2=0
x2+2xx2=0x(x+2)(x+2)=0x=1,2

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