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If x4 + x2y2 + y4 = 24 x2 + y2 + xy = 6 x3 - y3 = ? |
3 4 5 6\(\sqrt {3}\) |
6\(\sqrt {3}\) |
x4 + x2y2 + y4 = 24 x2 + y2 + xy = 6 x4 + x2y2 + y4 = 24 2(x2 + y2) = 10 x2 + y2 = 5 Put in x2 + y2 + xy = 6 5 + xy = 6 xy = 1 If x2 + y2 = 5 then x - y = \(\sqrt {5-2}\) x - y = \(\sqrt {3}\) x3 - y3 = (x-y)(x2 + y2 + xy) \(\sqrt {3}\) × 6 6\(\sqrt {3}\) |
