If a=\sqrta+1/\sqrta,y=\sqrta-1/\sqrta , then the value of x ^4 + y^ 2 - 2x ^2 y ^2 is:

Algebra and Applications Test 2

Question : 33 of 40

Marks: +1, -0

a=√a+1/√a,y=√a-1/√a

, then the value of

x ^4 + y^ 2 - 2x ^2 y ^2

is:

Solution:

a=√a+1/√a,y=√a-1/√a

Squaring both equations on both sides we get:

x^2=a+1/a+2

y^2=a+1/a-2

Squaring both the equations again

x^4=a^2+1/a^2+4+2+4/a+4a

y^4=a^2+1/a^2+4+2-4/a-4a

Substitute these values in equations

x ^4 + y^4 - 2x^ 2 y^ 2

we get,

x ^4 + y^4 - 2x^ 2 y^ 2=16

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