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Divide 29 into two parts so that the sum of the squares of the parts is 425. |
Answer» Let one of the number be ‘a’. Given, sum of two numbers is 29 and the sum of their squares is 425 ⇒ a2 + (29 – a)2 = 425 ⇒ a2 + 841 + a2 – 58a = 425 ⇒ a2 – 29a + 416 = 0 ⇒ a2 – 16a – 13a + 208= 0 ⇒ a(a – 16) – 13(a – 16) = 0 ⇒ (a – 13)(a – 16) = 0 ⇒ a = 13, 16 |
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