Chapter 9, Problem 3MPS

To determine

To Find: The integers.

Answer to Problem 3MPS

No solution

Explanation of Solution

Given: The sum of the square of the two consecutive even integers is $34$

Let the integers be $xandx+2$

Then

The sum of the square of the two consecutive even integers is $34$

i.e.

  ${(x)}^2+{(x+2)}^2=34$

Solving

  $\begin{array}{l}{x}^2+x^2+4x+4=34\\ 2x^2+4x+4=34\\ 2x^2+4x+4-34=0\\ 2x^2+4x-30=0\\ x^2+2x-15=0\\ x=3,-5\end{array}$

The problem has no solution as the value of $x$ is odd but we need the consecutive even integers.