Question

divide the number 18 into two positive parts so that thesum of their squares is equal to 15 times of the larger parts

Answer 1

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