Question

The sum of the squares of two consecutive natural numbers is $313$. Then the numbers will be:

• A. $12,13$
• B. $13,-12$
• C. $12,-13$
• D. $-12,-13$

Answer 1

Answer: (A)

$12,13$

Given: sum of the squares of two consecutive natural numbers is 313

To find the numbers

Sol: Let 1 number be $x$. Since the numbers are consecutive, the other number would be $x+1$.

Square both and add together to equal 313.

$x^2+(x+1{)}^2=313$

$x^2+x^2+2x+1=313$

$2x^2+2x-312=0$

$x^2+x-156=0$

$(x-12)(x+13)=0$

$x=12,x=-13$

given numbers are natural . so $x=12$ and $x+1=13$ are the two numbers.