यदि `x=a^(1/2)+a^(-1/2),t=a^(1/2)-a^(-1/2)` है तो `(x^(4)-x^(2)y^(2)-1)+(y^(4)-x^(2)y^(2)+1)` का मान है

Options

A. 13
B. 12
C. 14
D. 16

Answer

D

Explanation

According to the question
`x=sqrt(a)+1/(sqrt(a))` & `y=sqrt(a)-1/(sqrt(a))`
`:. x^(4)-x^(2)y^(2)-1+y^(4)-x^(2)y^(2)+1`
`=x^(4)-2x^(2)y^(2)+y^(4)`
`=[x^(2)-y^(2)]^(2)`
`[(sqrt(a)+1/(sqrt(a)))^(2)-(sqrt(a)-1/(sqrt(a)))^(2)]^(2)`
`=[a+1/a+2-a-1/a+2]^(2)`
`=[4]^(2)=16`