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

Options

A. `-9/8`
B. `-25/8`
C. `7/8`
D. `11`

Answer

C

Explanation

`2x+2/x=3`
`implies x+1/x=3/2`
Taking cube on the sides
`=(x+1/x)^(3)=(3/2)^(3)`
`{:|((x+1/x=a),(x^(3)+1/(x^(3))=a^(3)-3a)):}`
`x^(3)+1/(x^(3))+3(x+1/x)=27/8`
`implies x^(3)+1/(x^(3))+3xx3/2=27/8`
`implies x^(3)+1/(x^(3))=27/8-9/2`
`=(27-36)/8=(-9)/8`
`:. x^(3)+1/(x^(3))+2=(-9)/8+2`
`=x^(3)+1/(x^(3))+2=(-9+16)/8=7/8`