Beautiful yet puzzling equations!!!

Algebra Level 4

if (x-y)(x+2y)(2x+y) = 20 AND x^2 + xy + y^2 = 7

then find positive integral value of x assuming y is also positive.Please dont guess


The answer is 2.

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1 solution

Reynan Henry
Apr 1, 2015

x 2 + x y + y 2 = 7 x^{2} + xy + y^{2} = 7 it means that x 2 < 7 x^{2} < 7 so x = 1 x = 1 or 2 2 put x = 1 x=1 and you will get y > x y > x put x = 2 x=2 you will get y = 1 y=1

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