यदि `x+(1)/(x)=5` हो,तो `(x^(4)+(1)/(x^(2)))/(x^(2)-3x+1)` का मान कितना होगा?

Options

A. 70
B. 50
C. 110
D. 55

Answer

D

Explanation

`x+(1)/(x)=5rArrx^(2)-5x+1=0`
`rArrx^(2)-3x+1=2x`
`therefore(x^(4)+(1)/(x^(2)))/(x^(2)3x+1)=(1)/(2)((x^(4)+(1)/(x^(2)))/(x))`
`=(1)/(2)(x^(3)+(1)/(x^(3)))`
`=(1)/(2)[(x+(1)/(x))^(3)-3(x+(1)/(x))]`
`=(1)/(2)(125-3xx5)=(1)/(2)xx110=55`