If a(x + y) = b(x - y) = 2ab, then the value of 2($$x^{2} + y^{2}$$) is
Given : a(x + y) = b(x - y) = 2ab
=> $$a(x+y)=2ab$$
=> $$(x+y)=2b$$
Squaring both sides,
=> $$(x+y)^=(2b)^2$$
=> $$x^2+y^2+2xy=4b^2$$ -----------(i)
Similarly, $$(x-y)=2a$$
Squaring both sides,
=> $$(x-y)^=(2a)^2$$
=> $$x^2+y^2-2xy=4a^2$$ -----------(i)
Adding equations (i) and (ii), we get :
=> $$2x^2+2y^2=4a^2+4b^2$$
=> $$2(x^2+y^2)=4(a^2+b^2)$$
=> Ans - (D)
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