Chapter 1.5, Problem 2GP

To determine

What are the integers. Use a strategy to solve the problem.

Answer to Problem 2GP

  $27,29\text{and -27,-29}$

Explanation of Solution

Given :

The product of two consecutive non-negative odd integers is 783.

In order to find what are the integers, let first odd number be x , this implies that the next odd number be x+ 2, now there product is 783 as given in the question now solving it as shown below:

  $\begin{array}{l}x\left(x+2\right)=783\\ x^2+2x=783\\ x^2+2x-783=0\\ \text{now, spliting the expression}\\ \left(x-27\right)\left(x+29\right)=0\\ x-27=0,x+29=0\\ x-27=0\\ x=27\\ x+29=0\\ x=-29\\ \text{Now we assumed that the number be }x\text{and }x+2.\\ \text{if }x=27,\text{then }x+2=27+2=29\\ \text{the integers are 27 and 29}\\ \text{also if }x=-29,\text{then }x+2=-29+2=-27\\ \text{the integers are -29 and -27}\end{array}$

So, the integers are $27,29\text{and -27,-29}$ .