Question 89

If $$(x+y)^{2}=xy+1$$ and $$x^3 - y^3 = 1$$, then what is the value of x - y?

Solution

Given : $$(x+y)^{2}=xy+1$$

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

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

Also, $$x^3 - y^3 = 1$$

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

Substituting value from equation (i), we get :

=> $$(x-y)(1)=1$$

=> $$x-y=1$$

=> Ans - (A)

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