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Question

If x2+1x=313 and x > 1 , then find x31x3.

A
62627
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B
262627
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C
132627
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D
422627
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Solution

The correct option is A 262627
x2+1x=313

=>x+1x=103

Squaring both sides,

(x+1x)2=(103)2

=>x2+(1x)2+2(x)(1x)=1009

=>x2+(1x)2=10092

=>x2+(1x)2=829

Now, (x1x)2=x2+(1x)22(x)(1x)
=(8292)

=(649)

(x1x)=(649)

=(83)

=223

Now, (x31x3)=(x1x)[(x2+(1x)2+(x)(1x)]

=(83)(829+1)

=(83)(919)
=72827

=26267


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