If x ^2 + y^ 2 + 1/x^2+1/y^2 = 4, then the value of x^2+ y^2 is

SSC CGL Model Paper 9

Question : 74 of 100

Marks: +1, -0

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

, then the value of

x^2+ y^2

Solution:

(x^2-2+1/x^2)+(y^2-2+1/y^2)=0

(x-1/x)^2+(y-1/y)^2=0

x-1/x=0⇒x^2-1=0⇒x±1

Similarly, y = ± 1

x ^2 + y ^2 = 2

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