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

Answers ( )

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    2022-01-21T08:18:34+00:00

    Answer:

    [tex]x-8[/tex],  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.

    Question asked:

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

    Solution:

    [tex]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[/tex]

    [tex]x-8[/tex]  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 [tex]\times[/tex] 9 = 72

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