Question

the sum of two consecutive integers is 48. find the integer
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Answer 1

Two consecutive even integers are 2n and 2(n+1), where n = an integer.

2n*2(n+1) = 48 (The product of the two integers is 48)

4n2+4n-48=0(Multiply out, subtract 48 from both sides)

n2+n-12=0(Divide both sides by 4)

(n+4)(n-3)=0 (Factor the quadratic)

n= -4 and +3

For n= -4, 2n = -8 and 2(n+1) = -6. (-8)(-6) = 48

For n=3, 2n = 6 and 2(n+1) = 8. (8)(6) = 48

There are two answers: -8 and -6, and 6 and 8.