We can also solve it algebraically, may be in a quicker way. We know (x - y)² = (x + y)² - 4xy. That means, (x - y)² = 6² - 4 (36) = -108. So (x - y) = ± √ (-108) = ± 6√ (-3) = ± 6i√ 3. We have now (x + y ) = 6 and (x -y) = ± 6i√ 3. Therefore, x1 = ½ (6 + 6i√ 3) = 3(1 + i√ 3) and x2 = ½ (6 - 6i√ 3) , i.e = 3(1 - i√ 3). Using these values of x1 and x2 in eqn. (1), our y1 and y2 will be 3(1 - i√ 3) and 3(1 + i√ 3) respectively.
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No real solutions. Equation 1 squared is x^2 + 2xy + y^2 = 36. Eq 2 says xy = 36. Substituting this leads to x^2 + 72 + y^2 = 36. This becomes x^2 + y^2 = -36 This never happens in the real world.
