# Thread: How to solve these 3 equations in 3 unknowns (invloving square root) ?

1. ## How to solve these 3 equations in 3 unknowns (invloving square root) ?

Hi

I want to solve these 3 equations:

$\dfrac{x}{\sqrt{x^2+y^2+z^2}}=0.6$

$\dfrac{y}{\sqrt{x^2+y^2+z^2}}=0.3$

$\dfrac{z}{\sqrt{x^2+y^2+z^2}}=0.75$

How to solve them?
Can I square an equation?

2. Originally Posted by Liverpool
Hi

I want to solve these 3 equations:

$\dfrac{x}{\sqrt{x^2+y^2+z^2}}=0.6$

$\dfrac{y}{\sqrt{x^2+y^2+z^2}}=0.3$

$\dfrac{z}{\sqrt{x^2+y^2+z^2}}=0.75$

How to solve them?
Can I square an equation?
I assume the numbers on the right hand side of each equation are decimal approximations (because the sum of the squares should equal 1 and it doesn't) ...?

Your three equations can be written in the form $\displaystyle \frac{0.6}{x} = \frac{0.3}{y} = \frac{0.75}{z}$ and from this you can get three simple equations to solve for x, y and z.

3. Why the sum must be 1?

4. Originally Posted by Liverpool
Why the sum must be 1?
Square each equation and add. The left hand side is exactly equal to 1. Therefore the right hand side should equal 1 (but it doesn't).

5. Thanks.