Question 156843
The product of two consecutive odd integer is 1 less than 4 times their sum find the two integers
:
The two consecutive odd integers: x, (x+2)
:
write an equation for what it says:
x(x+2) = 4[x + (x+2)] -1
:
x^2 + 2x = 4(2x+2) - 1
:
x^2 + 2x = 8x + 8 - 1
;
x^2 + 2x = 8x + 7
Arrange as a quadratic equation
x^2 + 2x - 8x - 7 = 0
:
x^2 - 6x - 7 = 0
Factor
(x-7)(x+1) = 0
:
x = +7
and
x = -1
:
The integers: 7, 9 and -1,+1
;
;
Check solution in the statement:
"The product of two consecutive odd integer is 1 less than 4 times their sum
x=7: 7*9 = 4(16) - 1
x=-1: -1*1 = 4(-1+1) - 1