SOLUTION: Please help me with these. I need to know the equation and why or how it is set up the way it is. Thanks!! The sum of two numbers is eleven. The sum of the squares of the two num

Question 922633: Please help me with these. I need to know the equation and why or how it is set up the way it is. Thanks!!
The sum of two numbers is eleven. The sum of the squares of the two numbers is eighty-five. Find the two numbers.
and
The sum of two numbers is eleven. The sum of the squares of the two numbers is eighty-five. Find the two numbers

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
These kind of problems are done the same way.
let a & b be the two numbers. Write an equation for each statement
:
"The sum of two numbers is eleven."
a + b = 11
b = (-a+11); use this form for substitution
:
"The sum of the squares of the two numbers is eighty-five."
a^2 + b^2 = 85
replace b with (-a+11)
a^2 + (-a+11)^2 = 85
FOIL (-a+11)(-a+11)
a^2 + a^2 - 11a - 11a + 121 = 85
combine like terms
2a^2 - 22a + 121 - 85 = 0
a quadratic equation, we can solve
2a^2 - 22a + 36 = 0
simplify, divide by 2
a^2 - 11a + 18 = 0
Factors to
(a-2)(a-9) = 0
two solutions
a = 2, then b = 9
a = 9, then b = 2
" Find the two numbers." 2 & 9
:
Did you find you could follow what we did here?

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