Answer:
[tex]-3, -1, 1[/tex] or [tex]3, 5, 7[/tex]
Step-by-step explanation:
Let first consecutive odd integer = [tex]x[/tex]
Second consecutive odd integer = [tex]x+2[/tex]
Third consecutive odd integer = [tex]x+4[/tex]
"Product of the first two is equal to one more than twice the third" can be written as:
[tex]x(x+2)=1+2(x+4)[/tex]
[tex]x^2+2x=1+2x+8[/tex] (expand brackets)
[tex]x^2+2x=9+2x[/tex] (combine like terms)
[tex]x^2=9[/tex]
[tex]x=\pm3[/tex]
∴ Consecutive integers = [tex]-3, -1, 1[/tex] or [tex]3, 5, 7[/tex]
Hope this helps :)
