The sum of the squares of three consecutive natural numbers is 149. Find the numbers.

Given:

The sum of the squares of three consecutive natural numbers is 149.

 To do:

We have to find the numbers.

Solution:

Let the three consecutive natural numbers be $x-1$, $x$ and $x+1$.

According to the question,

$(x-1)^2+(x)^2+(x+1)^2=149$

$x^2-2x+1+x^2+x^2+2x+1=149$

$3x^2+2-149=0$

$3x^2-147=0$

$3(x^2-49)=0$

$x^2-49=0$

$(x)^2-(7)^2=0$

$(x+7)(x-7)=0$

$x+7=0$ or $x-7=0$

$x=-7$ or $x=7$

$-7$ is not a natural number. Therefore, $x=7$.

$x-1=7-1=6$ and $x+1=7+1=8$

The required natural numbers are $6$, $7$ and $8$. 

Tutorialspoint

e

Updated on: 10-Oct-2022

90 Views

Kickstart Your Career

Get certified by completing the course

Get Started