यदि `4a- 4/a+3=0` है तो `a^(3)-1/(a^(3))+3=?`

Options

A. `7/16`
B. `3/16`
C. `21/64`
D. `21/16`

Answer

C

Explanation

Given `4a4/a+3=0`
Find : `a^(3)-1/(a^(3)+3)=?`
`implies 4a-4/a=-3`
`implies a-1/a=(-3)/4`
`implies (a-1/a)^(3)=((-3)/4)^(3)`
[cubing both sides]
`implies a^(3)-1/(a^(3))-3axx1/a(a-1/a)=(-27)/64`
`implies a^(3)-1/(a^(3))-3xx (3/4)=(-27)/64`
`implies a^(3)-1/(a^(3))=(-27)/64-9/4+3`
`implies (192-171)/64impliesa^(3)-1/(a^(3))+3=21/64`