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Find the two positive numbers whose sum is 15 and sum of whose squares are minimum. |
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Answer» x + y = 15 ⇒ y = 15 - x s = x2 + y2 ⇒ s = x2 + (15 - x)2 ds/dx = 2x + 2(15 - x) (-1) ds/dx = 0 2x – 30 + 2x 0 = 4x - 30 x = 30/4 = 7.5 d2s/dx2 = 2 + 2 = 4 > 0 ∴ x = 7.5 require no is y = 7.5 & x = 7.5 |
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