SOLUTION: The equation below comes from a formula that Euclid discovered while studying right triangles. (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2 Prove that the equation is true.(hint: try using

Algebra ->  Pythagorean-theorem -> SOLUTION: The equation below comes from a formula that Euclid discovered while studying right triangles. (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2 Prove that the equation is true.(hint: try using       Log On


   

Question 1181911: The equation below comes from a formula that Euclid discovered while studying right triangles.
(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2
Prove that the equation is true.(hint: try using a difference of squares)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2%2By%5E2%29%5E2=%28x%5E2-y%5E2%29%5E2%2B%282xy%29%5E2
Prove that the equation is true.(hint: try using a difference of squares)
%282xy%29%5E2=%28x%5E2%2By%5E2%29%5E2-%28x%5E2-y%5E2%29%5E2
%282xy%29%5E2=x%5E4+%2B+2+x%5E2+y%5E2+%2B+y%5E4-%28x%5E4+-+2+x%5E2+y%5E2+%2B+y%5E4%29
%282xy%29%5E2=x%5E4+%2B+2x%5E2+%2Ay%5E2+%2B+y%5E4-x%5E4+%2B+2x%5E2%2Ay%5E2+-+y%5E4
%282xy%29%5E2=2x%5E2+%2Ay%5E2+%2B+2x%5E2%2Ay%5E2
%282xy%29%5E2=4x%5E2%2Ay%5E2
%282xy%29%5E2=%282xy%29%5E2