Question

The sum of the square of two consecutive natural number is $313$. Find the numbers.

Answer 1

We have,

Let the two consecutive number $=xandx+1$

So,

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

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

$\Rightarrow 2x^2+2x=313-1$

$\Rightarrow 2x^2+2x=312$

$\Rightarrow x^2+x=156$

$\Rightarrow x^2+x-156=0$

$\Rightarrow x^2+(13-12)x-156=0$

$\Rightarrow x^2+13x-12x-156=0$

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

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

If,

$x+13=0,x=-13$

$x-12=0,x=12$

Then,

$x=12$

$x+1=13$

Hence, this is the answer.