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Divide 29 into Two Parts So that the Sum of the Squares of the Parts is 425. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

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

⇒ 𝑥2 + (29 - 𝑥)2 = 425

⇒ 2𝑥2 - 58𝑥 + 841 - 425 = 0

⇒ 2𝑥2 - 58𝑥 + 416 = 0

⇒ 2[𝑥2 - 29𝑥 + 208] = 0

⇒ 𝑥2 - 29𝑥 + 208 = 0

⇒ 𝑥2 - 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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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.
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