A Pick from Mathlinks

AIEEE 2015 Questions › Olympiad Stuff questions › A Pick from Mathlinks

Solve for positive reals (x,y,z)

z^2+2xyz=1
3x^2y^2+3y^2x=1+x^3y^4
z+zy^4+4y^3=4y+6y^2z

It's been a while no -one has really given any elaborate soln for this.....

#Mathematics #Olympiad Stuff

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Devil ·2009-12-20 08:26:06

The reason I posted it here was that some guy in mathlinks used an useful substtituiton of putting x as tanÎ¸...but my query is why such a substitution - I mean what hinted at that?

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Lokesh Verma ·2009-12-21 08:05:30

The hint of such a substitution comes from equation 2...

which is also a quadratic in y²

Think of the formula of tan 3k... specially in the second equation..

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A Pick from Mathlinks

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