The sum of two natural numbers is 12 and the sum of their squares is 74. Find the numbers.
Quadratic Equations
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The sum of two natural numbers is 12 and the sum of their squares is 74. Find the numbers.

KnowledgeBoat · Accepted Answer

Let the numbers be x and y. Given, Sum of numbers = 12. ⇒ x + y = 12 ⇒ x = 12 - y .........(1) Given, Sum of their squares is 74. ⇒ x2 + y2 = 74 .........(2) Substituting value of x from equation (1) in equation (2), we get : ⇒ (12 - y)2 + y2 = 74 ⇒ (12)2 + y2 - 2 × 12 × y + y2 = 74 ⇒ y2 + y2 - 24y + 144 = 74 ⇒ 2y2 - 24y + 144 - 74 = 0 ⇒ 2y2 - 24y + 70 = 0 ⇒ 2y2 - 10y - 14y + 70 = 0 ⇒ 2y(y - 5) - 14(y - 5) = 0 ⇒ (2y - 14) (y - 5) = 0 ⇒ (2y - 14) = 0 or (y - 5) = 0 [Using zero-product rule] ⇒ 2y = 14 or y = 5 ⇒ y = or y = 5 ⇒ y = 7 or y = 5 Substituting value of y in equation (1), we get : Case 1: If y = 7, x = 12 - 7 = 5. Case 2: If y = 5, x = 12 - 5 = 7. Hence, the two natural numbers are 5 and 7.

Mathematics

The sum of two natural numbers is 12 and the sum of their squares is 74. Find the numbers.

Quadratic Equations

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