If x+1/x=17, then what is the value of \frac{x^4+1/x^2}{x^2-3x+1}?

SSC CGL Model Paper 12

Question : 62 of 100

Marks: +1, -0

x+1/x=17

, then what is the value of

{x^4+1/x^2}/{x^2-3x+1}?

Solution:

x+1/x=17

⇒x^2+1/x^2+2=289

⇒x^2+1/x^2=287

∴

{x^4+1/x^2}/{x^2-3x+1}

={x[x^3+1/x^3]}/{x[x- 3+{1}/x]}

={(x+1/x)(x^2+1/x^2-1)}/{x+1/x-3}

={17×(287-1)}/{17-3}=2431/7

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