Chapter 4.8, Problem 4P

To determine

To find two consecutive odd integers .

Answer to Problem 4P

The two consecutive odd integers are $7$ and $9$ or $-9$ and $-7$ .

Explanation of Solution

Given information: The sum of whose square is $130$ .

Calculation: The two consecutive odd integers are obtained as,

Let $x$ is first number,

  $x+2$ is second number.

therefore, according to question,

  $\begin{array}{l}{x}^2+{\left(x+2\right)}^2=130\\ x^2+x^2+2\cdot x\cdot 2+2^2=130\\ 2x^2+4x+4=130\\ 2x^2+4x+4-130=0\\ 2x^2+4x-126=0\\ 2\left(x^2+2x-63\right)=0\\ x^2+2x-63=0\\ x\left(x-7\right)+9\left(x-7\right)=0\\ \left(x-7\right)\left(x+9\right)=0\\ x=7,-9\end{array}$

If $x=7$ , $x+2=7+2=9$

If $x=-9$ , $x+2=-9+2=-7$

Hence, the two consecutive odd integers are $7$ and $9$ or $-9$ and $-7$ .