SOLUTION: separate 18 into two parts such that twice the sum of their squares is 5 times their product. the answers are given by:12and 6.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: separate 18 into two parts such that twice the sum of their squares is 5 times their product. the answers are given by:12and 6.      Log On


   

Question 805325: separate 18 into two parts such that twice the sum of their squares is 5 times their product.
the answers are given by:12and 6.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the numbers be x & y
produst = xy
sum of squares = x^2+y^2

2(x^2+y^2)=5xy
x^2+y^2=(5/2)xy
x^2+y^2+2xy = (5/2)xy +2xy
(x+y)^2=(9/2)xy
18^2=(9/2)xy
2*324/9 =xy
xy=72
x=72/y
72/y + y=18
72+y^2=18y
y^2-18y+72=0
y^2-12y-6y+72=0
(y-12)-6(y-12)=0
y=6 OR 12
the lengths are 6 & 12