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) [tex]x^2+2x=-1+4(2x+2)[/tex] [tex]x^2+2x=-1+8x+8[/tex] [tex]x^2+2x=8x+7 minus (8x+7) from both sides [tex]x^2-6x-7=0[/tex] 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)
