Question 148935
Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third.
:
Let the three consecutive numbers be x, (x+1), (x+2)
:
Write an equation for this statement:
"product of the first and third, minus the second,is 1 more than 4 times the third."
x(x+2) - (x+1) = 4(x+2) + 1
:
x^2 + 2x - x - 1 = 4x + 8 + 1
:
x^2 + x -1 = 4x + 9
:
Arrange as a quadratic equation on the left
x^2 + x - 4x - 1 - 9 = 0
:
x^2 - 3x - 10 = 0
Factors to:
(x-5)(x+2) = 0
Positive solution wanted
x = +5, 6, 7 are the 3 numbers
;
:
Check solution in the statement
"product of the first and third, minus the second,is 1 more than 4 times the third."
5*7 - 6 = 4(7) + 1
35 - 6 = 28 + 1