#### Question

Divide 29 into two parts so that the sum of the squares of the parts is 425.

#### 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

⇒ 𝑥^{2} + (29 - 𝑥)^{2} = 425

⇒ 2𝑥^{2} - 58𝑥 + 841 - 425 = 0

⇒ 2𝑥^{2} - 58𝑥 + 416 = 0

⇒ 2[𝑥^{2} - 29𝑥 + 208] = 0

⇒ 𝑥^{2} - 29𝑥 + 208 = 0

⇒ 𝑥^{2} - 13𝑥 - 16𝑥 + 208 = 0 [By the method of factorisation]

⇒ 𝑥(𝑥 - 13) - 16(𝑥 - 13) = 0

⇒ (𝑥 - 13)(𝑥 - 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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#### APPEARS IN

Solution Divide 29 into Two Parts So that the Sum of the Squares of the Parts is 425. Concept: Solutions of Quadratic Equations by Factorization.