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Question Number 105023 by bemath last updated on 25/Jul/20

(((x^2 −y^2 )^2 )/((1−x^2 )(y^2 −1)))+(((1−x^2 )^2 )/((x^2 −y^2 )(y^2 −1)))+(((y^2 −1)^2 )/((1−x^2 )(x^2 −y^2 )))=

(x2−y2)2(1−x2)(y2−1)+(1−x2)2(x2−y2)(y2−1)+(y2−1)2(1−x2)(x2−y2)=

Answered by john santu last updated on 25/Jul/20

(((x^2 −y^2 )^3 +(1−x^2 )^3 +(y^2 −1)^3 )/((1−x^2 )(y^2 −1)(x^2 −y^2 ))) [ set (x^2 −y^2 ) = u ; (1−x^2 ) = v ; (y^2 −1) = w ] ⇔((u^3 +v^2 +w^3 )/(uvw)) = (((u+w)^3 −3uw(u+w)+v^3 )/(uvw)) [ u+w = x^2 −1 = −v ] ⇒((−v^3 +3uvw+v^3 )/(uvw)) = ((3uvw)/(uvw)) = 3 (JS ★♠)

(x2−y2)3+(1−x2)3+(y2−1)3(1−x2)(y2−1)(x2−y2)[set(x2−y2)=u;(1−x2)=v;(y2−1)=w]⇔u3+v2+w3uvw=(u+w)3−3uw(u+w)+v3uvw[u+w=x2−1=−v]⇒−v3+3uvw+v3uvw=3uvwuvw=3(JS★♠)

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