Question

If ax = bc, by = ca, cz = ab, then find xyz.

Answer 1

ax=bc
x=bc/a
by=ca
y=ca/b
cz=ab
z=ab/c

Answer 2

$ax = bc$
$x = \frac{bc}{a}$

$by = ca$
$y = \frac{ca}{b}$

$cz = ab$
$z = \frac{ab}{c}$

$xyz$
$= \frac{bc}{a} * \frac{ca}{b} * \frac{ab}{c}$    [Substituting the values of x, y, z. ]
$= \frac{bccaab}{abc}$     [Multiplying the fractions. ]
$= \frac{aabbcc}{abc}$
$= \frac{a^{2}b^{2}c^{2}}{a^{1}b^{1}c^{1}}$
$= a^{2-1} * b^{2-1} * c^{2-1}$
$= a^{1} * b^{1} * c^{1}$
$= abc$

Hope this may help you.