SOLUTION: the product of two odd integers is five more than six times the lesser integer. find the integers?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: the product of two odd integers is five more than six times the lesser integer. find the integers?      Log On


   

Question 990299: the product of two odd integers is five more than six times the lesser integer. find the integers?
Found 2 solutions by macston, addingup:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solved for consecutive odd integers:
.
S=smaller integer; L=larger integer=S+2
S%2AL=6S%2B5
S%28S%2B2%29=6S%2B5
S%5E2%2B2S=6S%2B5
S%5E2-4S-5=0
S-5%29%28S%2B1%29=0
S-5=0 OR S%2B1=0
S=5 OR S=-1
.
For S=5:
L=S+2=5+2=7
ANSWER: The numbers are 5 and 7.
.
For S=-1:
L=S+2=-1+2=1
ANSWER: The numbers are -1 and 1.

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
x(x+2)=6x+5
x^2+2x=6x+5 subtract 6x, both sides
x^2-4x=5 Subtract 5, both sides
x^2-4x-5=0 Now factor the left side
(x-5)(x+1)=0 Separate into 2 equations
x-5=0 or x+1=0
x=5 or x=-1 Go back to the original equation and try each of these possible answers:
5(5+2)=6(5)+5= 35=35 We got our answer, x=5