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Find the Consecutive Even Integers Whose Squares Have the Sum 340. - CBSE Class 10 - Mathematics

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Question

Find the consecutive even integers whose squares have the sum 340.

Solution

Let the consecutive even integers be 2x and 2x + 2.

Then according to the given hypothesis,

(2𝑥)2 + (2𝑥 + 2)2 = 340

⇒ 8𝑥2 + 8𝑥 - 336 = 0

⇒ 𝑥2 + 𝑥 - 42 = 0

⇒ 𝑥2 + 7𝑥 - 6𝑥 - 42 = 0

⇒ 𝑥(𝑥 + 7) - 6(𝑥 + 7) = 0

⇒ (𝑥 + 7)(𝑥 - 6) = 0

⇒ x = -7 or x = 6

Considering, the positive integers of x.

⇒ x = 6; 2x = 12 and 2x + 2 = 14.

∴ The two consecutive even integers are 12 and 14.

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Solution Find the Consecutive Even Integers Whose Squares Have the Sum 340. Concept: Solutions of Quadratic Equations by Factorization.
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