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Question
Divide 29 into two parts so that the sum of the squares of the parts is 425.
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Solution
Let the two parts be ‘x’ and 29 – x
⇒ Given that the sum of the squares of the parts is 425.
Then, by hypothesis, we have
⇒ ๐ฅ2 + (29 - ๐ฅ)2 = 425
⇒ 2๐ฅ2 - 58๐ฅ + 841 - 425 = 0
⇒ 2๐ฅ2 - 58๐ฅ + 416 = 0
⇒ 2[๐ฅ2 - 29๐ฅ + 208] = 0
⇒ ๐ฅ2 - 29๐ฅ + 208 = 0
⇒ ๐ฅ2 - 13๐ฅ - 16๐ฅ + 208 = 0 [By the method of factorisation]
⇒ ๐ฅ(๐ฅ - 13) - 16(๐ฅ - 13) = 0
⇒ (๐ฅ - 13)(๐ฅ - 16) = 0
⇒ x = 13 or x = 16
Case i: If x = 13; 29 - x = 29 - 13 = 16
Case ii: x = 16; 29 - x = 29 - 16 = 13
∴ The two parts that the sum of the squares of the parts is 425 are 13, 16.
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