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Question

Solve the quadratic equation by factorization method.

xx+1+x+1x=3415

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Solution

Given quadratic equation is
xx+1+x+1x=3415

15[x2+(x+1)2]=34[x(x+1)]

15[2x2+2x+1]=34[x2+x]

30x2+30x+15=34x2+34x

4x2+4x15=0

4x2+10x6x15=0

2x(2x+5)3(2x+5)=0

(2x+5)(2x3)=0

2x+5=0,2x3=0

x=32,52

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