यदि `a+1/a+1=0(a!=0)` है तो `(a^(4)-a)` का मान क्या होगा?

Options

A. 0
B. 11
C. 2
D. -1

Answer

A

Explanation

`a+1/a=1=0`
`a+1/a=-1`
Squaring both sides
`implies a^(2)+1/(a^(2))+2=1`
`impliesa^(2)+1/(a^(2))=-1`
`impliesa^(2)+1=(-1)/(a^(2))`……………i
`impliesa+1/a=-1` (given)
`:.a^(2)+1=-a` ………….ii
`implies-a=(-1)/(a^(2))`
From equation i and ii
`a^(3)=1`
`:. a^(3)-1=0`
`impliesa^(4)-a=a(a^(3)-1)=axx0=0`