Shhh,, 10 = 7.
Let a = x-y .... b = (x + y)^2 .... c = 4(x^2 - x y + y^2) .... u = a .... v = b-c
(u+sqrt{v})^3 = u^3 +3u^2 sqrt{v}+3uv+vsqrt{v}
(u-sqrt{v})^3 = u^3 -3u^2 sqrt{v}+3uv-vsqrt{v}
(a+sqrt{b - c})^3 = a\(a^2 +3b-3c)+(3a^2 +b-c)sqrt{b-c}
(a-sqrt{b - c})^3 = a\(a^2 +3b-3c)-(3a^2 +b-c)sqrt{b - c}
3a^2 +b-c = 3(x^2 -2xy+y^2)+x^2+2xy+y^2 -4(x^2 -xy+y^2) = 0
So:
(a + \sqrt{b - c})^3 = (a - \sqrt {b - c})^3
a + \sqrt{b - c} = a - \sqrt {b - c}
\sqrt {b - c} = 0
b - c = 0
b = c
(x + y)^2 = 4 (x^2 - x y + y^2)
x^2 + 2 x y + y^2 = 4 (x^2 - x y + y^2)
-3x^2+6xy-3y^2 = 0
(x - y)^2 = 0
x - y = 0
x = y
10 = 7
