jmc

Question

Given that 3x + y = 10 and x + 3y = 14, find 10x^2 + 12xy + 10y^2.

Accepted Answer

Note that align* 10x^2 + 12xy + 10y^2 &= (9x^2 + 6xy + y^2) + (x^2 + 6xy + 9y^2) &= (3x + y)^2 + (x + 3y)^2 &= 10^2 + 14^2 = 296align*.