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Question-200617




Question Number 200617 by sonukgindia last updated on 21/Nov/23
Answered by Frix last updated on 21/Nov/23
x+a=y^2   y+a=x^2   x−y=y^2 −x^2   x^2 −y^2 +x−y=0  (x−y)(x+y)+(x−y)=0  (x−y)(x+y+1)=0  y=x∨y=−(x+1)  Now it′s easy to do the rest.
$${x}+{a}={y}^{\mathrm{2}} \\ $$$${y}+{a}={x}^{\mathrm{2}} \\ $$$${x}−{y}={y}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} +{x}−{y}=\mathrm{0} \\ $$$$\left({x}−{y}\right)\left({x}+{y}\right)+\left({x}−{y}\right)=\mathrm{0} \\ $$$$\left({x}−{y}\right)\left({x}+{y}+\mathrm{1}\right)=\mathrm{0} \\ $$$${y}={x}\vee{y}=−\left({x}+\mathrm{1}\right) \\ $$$$\mathrm{Now}\:\mathrm{it}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{do}\:\mathrm{the}\:\mathrm{rest}. \\ $$

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