Question

Find two consecutive positive integers such that the sum of their squares is 365.

• A. 17,18
• B. 13,14
• C. 9,10
• D. 12,13

Answer 1

The correct option is B

13,14

Let the numbers be $xandx+1$

$x^2+(x+1{)}^2=365$

$\Rightarrow x^2+x^2+2x+1=365$

$\Rightarrow 2x^2+2x-364=0$

$\Rightarrow x^2+x-182=0$ (on dividing by 2)

$\Rightarrow x^2+14x-13x-182=0$

$\Rightarrow x=13or-14$

Since numbers are positive integers $x=13$

So, required consecutive numbers are $13and14$.