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Question Number 185972 by Michaelfaraday last updated on 30/Jan/23

Answered by Rasheed.Sindhi last updated on 30/Jan/23

x=(p)^(1/3) +(1/( (p)^(1/3) )) , y=(√p) +(1/( (√p) )) Show that y^2 −2=x(x^2 −3) x^3 =((p)^(1/3) +(1/( (p)^(1/3) )))^3 =p+(1/p)+3((p)^(1/3) +(1/( (p)^(1/3) ))) =p+(1/p)+3(x) p+(1/p)=x^3 −3x=x(x^2 −3)......(i) y^2 =((√p) +(1/( (√p) )))^2 =p+(1/p)+2 p+(1/p)=y^2 −2.............(ii) (i) & (ii): y^2 −2=x(x^2 −3)

x=p3+1p3,y=p+1pShowthaty2−2=x(x2−3)x3=(p3+1p3)3=p+1p+3(p3+1p3)=p+1p+3(x)p+1p=x3−3x=x(x2−3)......(i)y2=(p+1p)2=p+1p+2p+1p=y2−2.............(ii)(i)&(ii):y2−2=x(x2−3)

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