यदि `a+1/a=sqrt(3)` है तो `a^(52)+1/(a^(52))` का मान क्या होगा?

Options

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

Answer

A

Explanation

`a+1/a=sqrt(3)`
`a^(3)+1/(a^(3))=(sqrt(3))^(3)-3sqrt(3)`
`a^(6)=-1`
`a^(2)+1/(a^(2))=1`
then `a^(52)+1/(a^(52))=(a^(54))/(a^(2))+(a^(2))/(a^(54))`
`=((a^(6))^(9))/(a^(2))+(a^(2))/((a^(6))^(9))`
`=-1/(a^(2))-a^(2)=-(a^(2)+1/a^(2))`
then `a^(52)+1/(a^(52))=-1`