यद‌ि `x-1/x=1` है तो `(x^(4)-1/(x^(2)))/(3x^(2)+5x-3)` का मान ज्ञात करें।

Options

A. `1/4`
B. `1/2`
C. `3/4`
D. 0

Answer

B

Explanation

`x-1/x=1`
`implies (x^(4)-1/(x^(2)))/(3x^(2)-5x-3)`
Divide and multiply by `x`
`((x^(4))/x-1/(x^(3)))/((3x^(2))/x+(5x)/x-3/x)`
`=(x^(3)-1/(x^(3)))/(3x-3/x+5)implies(x^(3)-1/(x^(3)))/(3(x-1/x)+5)`
`implies x-1/x=1`
Take cube on both sides
`(x-1/x)^(3)=(1)^(3)`
`implies x^(3)-1/(x^(3))-3(x-1/x)=1`
`x^(3)-1/(x^(3)-3)=1`
`implies x^(3)-1/(x^(3))=4`
`= (x^(3)-1/(x^(3)))/(3(x-1/x)+5)=4/(3xx1+5)=4/8=1/2`