If x - y = 8 and xy = 5, find x2 + y2.
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We know that,
(x - y)2 = x2 - 2xy + y2
⇒ x2 + y2 = (x - y)2 + 2xy.
Substituting values we get,
⇒ x2 + y2 = (8)2 + 2 × 5⇒ x2 + y2 = 64 + 10⇒ x2 + y2 = 74.
Hence, x2 + y2 = 74.
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Without actually calculating the cubes, find the values of:
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(ii) (-28)3 + (15)3 + (13)3
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