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). Please help ASAP, thank you.

Answer 1

well, (x+y+z)^2 = x^2+y^2+z^2 + 2(xy+yz+zx)
see what you can do with that.

Answer 2

Answer is 11/14
steps......
1- first expression = second expression prepare equation1
4x+y-3z=0
2- first expression = third expression
2x+5y-3z=0
3- second expression = third expression
-4x+5y+z=0
5- now equation 1 - equation2
x=2y

6- multiply second equation by 2 and subtract from 1
z=3y

now use x=2y and z=3y in equation
(xy+yz+zx)/x^2+y^2+z^2
answer is 11/14