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

SSC CPO SI and ASI 2011 Paper

Question : 137 of 200

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}+y^{2}+ {1}/{x^{2}}+ {1}/{y^{2}}-4

=x^{2}+ {1}/{x^{2}}-2+y^{2}+ {1}/{y^{2}}-2=0

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

⇒(x- {1}/{x} )=0

and

(y- {1}/{y} )=0

So,

x=y=1

and the Value of

x^{2}+

y^{2}=1+1=2

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