Question 88

If x = 1 - y and $$x^2 = 2 - y^2$$, then what is the value of xy?

Solution

Given : $$x^2 = 2 - y^2$$

=> $$x^2+y^2=2$$ ----------(i)

Also, $$x=1-y$$

=> $$x+y=1$$

Squaring both sides, we get :

=> $$(x+y)^2=(1)^2$$

=> $$(x^2+y^2)+2xy=1$$

=> $$2+2xy=1$$ [Using (i)]

=> $$2xy=1-2=-1$$

=> $$xy=\frac{-1}{2}$$

=> Ans - (C)

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