## These product of two consecutive integers is 72. The equation x(x+1)=72 represents the situation, where x represents the smaller integer. Wh

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

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4 months 2022-01-21T08:17:01+00:00 1 Answer 0 views 0

$$x-8$$,  smaller integer is 8.

Step-by-step 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.

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