Question

Find two consecutive integers such that the sum of their squares is 145.

Answer 1

Answer: 8 and 9 or -9 and -8

Step-by-step explanation:

Let $x$ be the first of the two integers. Then, since the numbers are consecutive, $x+1$ is the other integer. We then know that the sum of the squares of $ x$ and $x+1$ is equal to 145. So, now we have the equation

$x^2+(x+1)^2=145$

which can be expanded and simplified to

$2x^2+2x+1=145$

which then gives us the quadratic equation

$2x^2+2x-144=0$

This can then be factored into

$2(x^2+x-72)=0  $

Which can be simplified further into

$2(x-8)(x+9)=0  $

So either $x=8$ or $x=-9$. This gives us two solutions: 8 and 9 or -9 and -8.

Hope this helps! CHEERS!