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

Options

A. 322
B. 126
C. 123
D. 113

Answer

C

Explanation

`x+1/x=3`
(Squaring both sides)
`x^(2)+1/(x^(2))=7`
On cubing both sides
`x^(3)+1/(x^(3))+3x xx 1/x(x+1/x)=27`
`implies x^(3)+1/(x^(3))+3xx3=27`
`x^(3)+1/(x^(3))=18`
`:. (x^(3)+1/(x^(3)))(x^(2)+1/(x^(2)))=18xx7`
`(x^(5)+1/(x^(5)))+(x+1/x)+126`
`(x^(5)+1/(x^(5))+3=126`
`=(x^(5)+1/(x^(5)))=123`