Tính a/x = b/y = c/z

The equation you provided is based on the condition \( \frac{a}{x} = \frac{b}{y} = \frac{c}{z} \). To find relationships among \( a, b, c, x, y, z \), we can use the equality of these ratios.

From the equation \( \frac{a}{x} = k, \frac{b}{y} = k, \frac{c}{z} = k \) for some constant \( k \), we can express:

- \( a = kx \)
- \( b = ky \)
- \( c = kz \)

Now, substituting these values into \( (ax + by + cz)^2 \):

\[
(ax + by + cz) = (kx^2 + ky^2 + kz^2) = k(xy + yz + zx)
\]

Now squaring this:

\[
(ax + by + cz)^2 = k^2(x^2 + y^2 + z^2)
\]

The equality shown in the original inequality becomes:

\[
\sqrt{(ax + by + cz)^2} = a^2 + b^2 + c^2
\]

This results in the conclusion that:

\[
\frac{a}{x} = \frac{b}{y} = \frac{c}{z}
\]

This shows the proportional relationships among \( a, b, c, x, y, z \). Thus, you can simplify it to prove the relationships.