When x2 + XY + y2 = 1, find the maximum and minimum value of x2 + Y2

When x2 + XY + y2 = 1, find the maximum and minimum value of x2 + Y2

From x2 + XY + y2 = 1, - xy = - 1 + (x2 + Y2) (1) From (x + y) 2 ≥ 0, X2 + Y2 ≥ - 2XY = - 2 + 2 (x2 + Y2), that is, X2 + Y2 ≥ - 2 + 2 (x2 + Y2), so - (x2 + Y2) ≥ - 2, so x2 + Y2 ≤ 2, that is, the maximum value of x2 + Y2 is 2

If the square of X + XY + y = 14 and the square of Y + XY + x = 28, then x + y =?
Why can the square of (x + y) + (x + y) - 42 = 0 be transformed into (x + y-6) (x + y + 7) = 0

By adding the two formulas, we can get: x ^ 2 + y ^ 2 + 2XY + X + y = 42 (x + y) ^ 2 + (x + y) = 42 (x + y) (x + y + 1) = 42. With the idea of substitution, we can see x + y as a whole. It's not hard to find (x + y) 1 = - 7 (x + y) 2 = 6. After substitution, we can solve a quadratic equation of two variables

Given X-Y = 5, xy = 14, find the square of (x + y)

Hello
(x + y) 2 = x2 + 2XY + y2 = x2-2xy + Y2 + 4xy = (X-Y) 2 + 4xy = the square of 5 + 4 * 14 = 25 + 56 = 81
Some 2's are squares. I can't understand them
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