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.

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) (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

RELATED QUESTIONS
Divide 12 into 2 parts such that the sum of their squares is... (answered by LinnW)

Divide 12 into two parts such that the sum of their squares is 74. We need to find the... (answered by htmentor)

Separate 45 into two parts such that 5 times the smaller is 6 less than twice the... (answered by Earlsdon)

If 50 is divided into two parts such that the sum of their reciprocals... (answered by Alan3354)

Divide 50 into two parts such that the sum of their reciprocals is 1/12. the numbers are (answered by mananth)

find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)

Find two numbers such that their sum multiplied by the sum of their squares is 65, and... (answered by mananth)

Separate 150 into two parts such that 4 times the larger exceeds 5 times the smaller by... (answered by checkley71)