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Find two consecutive odd positive integers …

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Find two consecutive odd positive integers sum of whose squares is 290

Posted by A. Sofiangelina 5 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 5 years, 10 months ago

Let one of the odd positive integer be x
then the other odd positive integer is x+2
their sum of squares = x² +(x+2)²
= x² + x² + 4x +4
= 2x² + 4x + 4
Given that their sum of squares = 290
⇒ 2x² +4x + 4 = 290
⇒ 2x² +4x = 290-4 = 286
⇒ 2x² + 4x -286 = 0
⇒ 2(x² + 2x - 143) = 0
⇒ x² + 2x - 143 = 0
⇒ x² + 13x - 11x -143 = 0
⇒ x(x+13) - 11(x+13) = 0
⇒ (x-11) = 0 , (x+13) = 0
Therfore , x = 11 or -13
We always take positive value of x
So , x = 11 and (x+2) = 11 + 2 = 13
Therefore , the odd positive integers are 11 and 13 .

1Thank You

Sneha Kumari 5 years, 10 months ago

Required numbers= 11 and 13

3Thank You

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