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

RRB Junior Engineer Stage 1 Model Papers 7

Question : 2 of 100

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x+1/x=17

, then what is the value of

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

Solution:

Here,

x+1/x=17

⇒{x^2+1}/x=17=x^2+1=17x

⇒x^2-17x+1=0

⇒x^2-3x+1=14x

∴{x^4+1/x^2}/{x^2-3x+1} =1/14({x^4+1/x^2}/x)=1/14(x^3+1/x^3)

⇒1/14[(x+1/x)^3-3(x+1/x)]

=1/14(4913-3×17)

⇒1/14×4862=2431/7

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