Question

Given the proportion (x+y)/3 = (y+z)/4 = (z+x)/5, determine the value of (xy+yz+zx)/x^2+y^2+z^2.

Answer 1

\[\frac{ x+y }{ 3 }=\frac{ y+z }{ 4 }=\frac{ z+x }{ 5 }=k(say)\]
x+y=3k (1)
y+z=4k (2)
z+x=5k (3)
adding
2(x+y+z)=12 k
x+y+z=6 k ....(4)
subtract (1),(2),(3) from (4)
z=3 k
x=2 k
y=k
put the values of x,y,z and get the result.

Answer 2

Thank you, it makes a lot more sense now!

Answer 3

yw