Question

These product of two consecutive integers is 72. The equation x(x+1)=72 represents the situation, where x represents the smaller integer. Which equation can be factored and solved for the smaller integer

Answer 1

`x-8`, smaller integer is 8.

Explanation:

Given:

The product of two consecutive integers is 72.

The equation x(x+1)=72 represents the situation, where x represents the smaller integer.

Question asked:

Which equation can be factored and solved for the smaller integer ?

Solution:

`x(x+1)=72\\\\ x^(2) +x=72\\ \\ By\ subtracting\ both\ sides\ by\ 72\\ \\ x^(2) +x-72=72-72\\ \\ x^(2) +x-72=0\\ \\ x^(2) +9x-8x-72=0\\ \\ Taking\ x+9\ as\ common \\ \\ x(x+9)-8(x+9)=0\\ \\ x+9=0,x-8=0\\ \\ x=-9,x=8`

`x-8` can be factored and solved for the smaller integer, and that is 8.

Two consecutive integers are 8 and 9 and their product is 8
`*` 9 = 72