Question

Find three consecutive positive integers such that the sum of their squares is 2354. What is the largest integer?

Answer 1

The largest integer is 29.

Explanation:

Let the consecutive positive integers are x, x+1 and x+2.

The square of sum of squares of three consecutive positive integers is 2354 such that,

`x^2+(x+1)^2+(x+2)^2=2354\\\\x^2+x^2+2x+1+x^2+4+4x=2354\\\\3x^2+6x+5=2354\\\\3x^2+6x- 2349=0`

It is a quadratic equation whose solution is given by :

x = 27 and x = -29

First positive integer = 27

Second positive integer = 27+1 = 28

Third positive integer = 27+2 = 29

Hence, the largest integer is 29.