A Nice Algebra Problem | 2 Different Methods | You should know this trick !!

A Nice Algebra Problem | 2 Different Methods | You should know this trick !!

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Mr. Gnome
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[miguelgnievesl]

In the 2nd method we have that x=1/x. Since x≠0 then we multiply on both sides by x and get x²=1. If we proceed in the same way for y, then y²=1.

[Andyyen-fqjh]

We can divide 4 into 2+2
And trans to another side
(X-1/X)^2 + (Y-1/Y)^2=0
So X=1/X, Y=1/Y
Sol: X^2+Y^2=2

[StaR-uwdc]

Nice solution as usual.
You can also use AM-GM for all 4 terms: (x^2+y^2+1/x^2+1/y^2)/4 >= = 1^(1/4) = 1 so all term are equal and are equal to 1 which implies: x^2+y^2 = 1+1 =2