1.

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 हैA. 13B. 12C. 14D. 16

Answer» Correct Answer - D
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`


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