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Question
Divide 29 into two parts so that the sum of the square of the parts is 425.
Solution
Let the parts be x and 29 - x
According to the problem
x2 + (29 - x)2 = 425
⇒ x2 + 841 + x2 - 58x - 425 = 0
⇒ 2x2 - 58x + 416 = 0
⇒ x2 - 29x + 208 = 0
⇒ x2 - 16x - 13x + 208 = 0
⇒ x(x - 16) - 13(x - 16) = 0
⇒ (x - 16) (x - 13) = 0
⇒ x - 16 = 0 or x - 13 = 0
⇒ x = 16 or x = 13
When x = 16 When x = 13
Then 29 - x = 13 Then 29 - x = 16
Hence, the parts are 16 and 13.
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