यदि `x^(4)+1/(x^(4))=119` और `xlt1` है तो `x^(3)+1/(x^(3))` का मान ज्ञात करें।

Options

A. `6sqrt(13)`
B. `8sqrt(13)`
C. `13sqrt(13)`
D. `10sqrt(13)`

Answer

D

Explanation

`x^(4)+1/(x^(4))=119, xgt1`
`:. x^(4)+1/(x^(4))+2=119+2=121`
`(x^(2)+1/(x^(2)))^(2)=(11)^(2)`
`x^(2)+1/(x^(2))=11`
`x^(2)+1/(x^(2))+2=11+2`
`(x+1/x)^(2)=13`
`x+1/x=sqrt(13)`
`implies` Taking cube both sides
`x^(3)+1/(x^(3))+3sqrt(13)=(sqrt(13))^(3)`
`x^(3)+1/(x^(3))+3sqrt(13)=13sqrt(13)`
`x^(3)+1/(x^(3))=10sqrt(13)`