two numbers differ by 8 and have a product 65. what are the numbers?
Answers
Step-by-step explanation:
Numbers m and n.
Differ by 8: n-m=8
Product is 65: mn=65
Find m and n.
The Differ equation gives n=m+8. Use this in the Product equation.
m(m+8)=65
m^2+8m-65=0, which we can factor, so let's do that:
(m+5)(m-13) ---- will that work? No. Gives -8m instead of +8m.
(m-5)(m+13) ---- Will that work? Yes. 13m-5m=8m, and product in const. term is -65.
OKAY, solution to the quadratic formed is m=5 or m=-13.
What about n?
n-m=8
n=m+8
For m=5, n=13.
For m=-13, n=-5.
ANSWER: Both solutions fit the description. Either the numbers are -5 and -13, or they are 5 and 13.
Answer:
let the number be x
the other number x-8
A/Q
x (x-8)=65
x ^2-8x=65
x^2-8x-65=0
x^2-13x+5x-65=0
x(x-13)+5 (x-13)=0
(x+5)(x-13)
Step-by-step explanation:
solve your will get 13 and 8