Solve for x : 4x^2-2(a^2+b^2)x+a^2b^2=0
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4x^2-2(a^2+b^2)x+a^2b^2=0
4x^2-2a^2x-2b^2x+a^2b^2=0
2x(2x-a^2)-b^2(2x-a^2)=0
(2x-a^2)(2x-b^2)=0
2x-a^2=0 or 2x-b^2=0
2x=a^2 or 2x=b^2
x=a^2/2 or x= b^2/2
4x^2-2a^2x-2b^2x+a^2b^2=0
2x(2x-a^2)-b^2(2x-a^2)=0
(2x-a^2)(2x-b^2)=0
2x-a^2=0 or 2x-b^2=0
2x=a^2 or 2x=b^2
x=a^2/2 or x= b^2/2
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