Question

Two consecutive positive integers, sum of whose squares is 365 are ___ and ___ .

• A. 13
• B. 14
• C. 15
• D. 16

Answer 1

Answer: (A), (B)

The correct options are
A

13

B

14

Let first number be $x$ and second number be $x+1$.

Given that
$x^2+(x+1{)}^2=365$
$x^2+x^2+1+2x=365$
$2x^2+2x–364=0$

Dividing equation by 2, we get
$x^2+x–182=0$

Factoring this equation, we obtain
x = 13, -14

Ignore negative number
First number = 13
Second number = $x+1$ = 14