SOLUTION: what are three consecutive positive numbers such that the product of the first and third, minus the second,is one more than five times the third

Question 365524: what are three consecutive positive numbers such that the product of the first and third, minus the second,is one more than five times the third
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three consecutive numbers, x, (x+1), (x+2)
:
Write an equation for just what it says:
"the product of the first and third, minus the second,is one more than five times the third"
:
x(x+2) - (x+1) = 5(x+2) + 1
x^2 + 2x - x - 1 = 5x + 10 + 1
x^2 + x - 1 = 5x + 11
Combine to form a quadratic equation
x^2 + x - 5x - 1 - 11 = 0
x^2 - 4x + 12 = 0
Factors to:
(x-6)(x-2) = 0
Two solutions
x = 6
x = 2
:
The numbers:
6, 7, 8
and
2, 3, 4
:
:
Check both solutions in the original equation
1st set: 6(8) - 7 = 5(8) + 1; a good solution
and
2nd set: 2(4) - 3 = 5(4) + 1; doesn't work
therefore
x = 6 is the only solution
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