Given x + y = 3, xy = 1, a + B = 5, ab = 3, M = ax + by, n = BX + ay, find the value of m ^ 2n ^ 2

Because x + y = 3, xy = 1, so x ^ 2 + y ^ 2 = (x + y) ^ 2-2xy = 3 ^ 2-2 * 1 = 7. Similarly, because a + B = 5, ab = 3, so a ^ 2 + B ^ 2 = 19, so Mn = (ax + by) (BX + ay) = ABX ^ 2 + A ^ 2XY + B ^ 2XY + aby ^ 2 = AB (x ^ 2 + y ^ 2) + (a ^ 2 + B ^ 2) xy = 3 * 7 + 19 * 1 = 40, so m ^ 2n ^ 2 = 1600

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