SOLUTION: The product of two positive consecutive integers is 41 more than their sum. Find the integers.
(I have gotten this far, but do not know how to show the next step.)
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Question 325632: The product of two positive consecutive integers is 41 more than their sum. Find the integers.
(I have gotten this far, but do not know how to show the next step.)
first integer = x
second integer = x+1
+ 41 more their sum =
=
x(x+1) = 41 + x + x + 1
=
x^2 + x = 42 + 2x
=
x^2 + x - (2x) = 42 + 2x - (2x)
=
x^2 - x = 42
=
x^2 - x - (42) = 42 - (42)
=
x^2 - x - 42 = 0
= ??????
Found 2 solutions by JBarnum, jessica43:
Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!
find 2 numbers that multiply to get 42 and add to get -1
-7 and +6 -7*6=-42 -7+6=-1
(x-7)(x+6)=0
x=7,-6
since x has to be possitive
then the numbers have to be 7,8
Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
You have set up the problem correctly, now all you have to do factor the trinomial x^2 - x - 42.
Factoring a trinomial is the opposite of the FOIL method. The factors will have this form:
(x A)(x B)
where A and B will be the factors of the third term (42). The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42. So these are our possibilities of A and B: 1&42, 2&21, 3&14, 6&7.
Now, we need to see what combination, when added, will equal -1 (since the second term of our trinomial is -x).
We know that one number must be negative because when multiplied they equal a negative number. So the only combination that could equal -1 when added is -7 and 6.
So:
x^2 - x - 42 = 0
(x-7)(x+6)= 0
So for this to equal zero, x = 7 or x = -6.
Since the problem states that the answer is a positive integer, x cannot equal -6.
So x=7 and the two consecutive integers are 7 and 8.
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