The sum of the squares of three consecutive odd numbers is 2531. Find the numbers.
Quadratic Equations
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Question

The sum of the squares of three consecutive odd numbers is 2531. Find the numbers.

KnowledgeBoat · Accepted Answer

Let the three consecutive odd numbers be x, x + 2, x + 4. Given, The sum of the squares of three consecutive odd numbers is 2531. ⇒ x2 + (x + 2)2 + (x + 4)2 = 2531 ⇒ x2 + x2 + (2)2 + 2 × 2 × x + x2 + (4)2 + 2 × 4 × x = 2531 ⇒ x2 + x2 + 4 + 4x + x2 + 16 + 8x = 2531 ⇒ 3x2 + 12x + 20 = 2531 ⇒ 3x2 + 12x + 20 - 2531 = 0 ⇒ 3x2 + 12x - 2511 = 0 ⇒ 3x2 + 93x - 81x - 2511 = 0 ⇒ 3x(x + 31) - 81(x + 31) = 0 ⇒ (3x - 81)(x + 31) = 0 ⇒ (3x - 81) = 0 or (x + 31) = 0 [Using zero-product rule] ⇒ 3x = 81 or x = -31 ⇒ x = or x = -31 ⇒ x = 27 or x = -31: Case 1: If x = 27, x + 2 = 27 + 2 = 29 x + 4 = 27 + 4 = 31 Case 2: If x = -31, x + 2 = -31 + 2 = -29 x + 4 = -31 + 4 = -27 Hence, the three consecutive odd numbers are 27, 29, 31 or -31, -29, -27.

Mathematics

The sum of the squares of three consecutive odd numbers is 2531. Find the numbers.

Quadratic Equations

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