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Find Two Consecutive Positive Integers, Sum of Whose Squares is 365 - Mathematics

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 Find two consecutive positive integers, sum of whose squares is 365

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Solution

Let the consecutive positive integers be x and x + 1.

Therefore, x2 + (x + 1)2 = 365

⇒ xx+ 1 + 2x = 365

⇒ 2x2 + 2x - 364 = 0

⇒ x- 182 = 0

⇒ x+ 14x - 13x - 182 = 0

⇒ x(x + 14) -13(x + 14) = 0

⇒ (x + 14)(x - 13) = 0

Either x + 14 = 0 or x - 13 = 0,

⇒ x = - 14 or x = 13
Since the integers are positive, x can only be 13.
∴ x + 1 = 13 + 1 = 14
Therefore, two consecutive positive integers will be 13 and 14.
Concept: Solutions of Quadratic Equations by Factorization
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APPEARS IN

NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.2 | Q 4 | Page 76
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