# Math Help - good question

1. ## good question

What is the value of
$\frac{x + y + z}{a + b +c}

$

$x^2 + y^2+ z^2=15

$

$a^2 + b^2+ c^2=25$

$ax +by + cz = 20$

2. Add the first and the second equalities and substract 2 times the third:

$x^2+y^2+z^2+a^2+b^2+c^2-2ax-2by-2cz=0$

$(x-a)^2+(y-b)^2+(z-c)^2=0\Rightarrow x=a, \ y=b, \ z=c$

Then $\frac{x+y+z}{a+b+c}=\frac{a+b+c}{a+b+c}=1$

3. Magnificent solution, red-dog!

*cheers* . *applause*