Given that | X-Y + 1 | and X2 + 8x + 16 are opposite to each other, find the value of x2 + 2XY + Y2

Given that | X-Y + 1 | and X2 + 8x + 16 are opposite to each other, find the value of x2 + 2XY + Y2

∫||x-y + 1|and x2 + 8x + 16 are opposite numbers, and |||x-y + 1|and (x + 4) 2 are opposite numbers, that is ||x-y + 1| + (x + 4) 2 = 0, | X-Y + 1 = 0, x + 4 = 0, the solution is x = - 4, y = - 3. When x = - 4, y = - 3, the original formula = (- 4-3) 2 = 49

Given that | X-Y + 1 | and X2 + 8x + 16 are opposite to each other, find the value of x2 + 2XY + Y2

∫||x-y + 1|and x2 + 8x + 16 are opposite numbers, and |||x-y + 1|and (x + 4) 2 are opposite numbers, that is ||x-y + 1| + (x + 4) 2 = 0, | X-Y + 1 = 0, x + 4 = 0, the solution is x = - 4, y = - 3. When x = - 4, y = - 3, the original formula = (- 4-3) 2 = 49

Solving equation (x2 + Y2) 2 + 1 = x2 + Y2 + 2XY

Expand x ^ 4 + 2x ^ 2Y ^ 2 + y ^ 4 + 1 = x ^ 2 + y ^ 2 + 2XY,
Move items and group them into (x ^ 4-x ^ 2 + 1 / 4) + (y ^ 4-y ^ 2 + 1 / 4) + 2 [(XY) ^ 2-xy + 1 / 4] = 0,
The factorization results in (x ^ 2-1 / 2) ^ 2 + (y ^ 2-1 / 2) ^ 2 + 2 (XY-1 / 2) ^ 2 = 0,
Because (x ^ 2-1 / 2) ^ 2 > = 0, (y ^ 2-1 / 2) ^ 2 > = 0, (XY-1 / 2) ^ 2 > = 0,
So we can get x ^ 2-1 / 2 = 0, y ^ 2-1 / 2 = 0, XY-1 / 2 = 0,
The solution is x = y = √ 2 / 2 or x = y = - √ 2 / 2