Question

The product of two consecutive odd intergers is 1 less than four times thier sum. Find the two integers.

Answer 1

consecutive odd integers are 2 apart
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum

x(x+2)=-1+4(x+x+2)

`x^2+2x=-1+4(2x+2)`

`x^2+2x=-1+8x+8`

`image`
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7

x+1=0
x=-1

so the x can be 7 or -1
the other number (x+2) can be 7 or 1

test each

7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true


-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true



the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)