If the real numbers x, y satisfy the equation 2x + x2 + x2y2 + 2 = - 2XY, then the value of X + y is () A. 1B. 0C. 1D. 2 | Math enthusiast | Mathematical art

If the real numbers x, y satisfy the equation 2x + x2 + x2y2 + 2 = - 2XY, then the value of X + y is () A. 1B. 0C. 1D. 2

∵ 2x + x2 + x2y2 + 2 = - 2XY, ∵ (x + 1) 2 + (XY + 1) 2 = 0. ∵ x + 1 = 0, XY + 1 = 0. The solution is x = - 1, y = 1. ∵ x + y = 0

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