If a^x = bc, b^y = ca, , c^z = ab, then xyz= - Vidyadip

MCQ

If ${a^x} = bc,{b^y} = ca,\,{c^z} = ab,$ then $xyz$=

A
$0$
B
$1$
C
$x + y + z$
✓
$x + y + z + 2$

✓

Answer

Correct option: D.

$x + y + z + 2$

d
(d) ${a^x}.{b^y}.{c^z} = bc.ca.ab = {a^2}{b^2}{c^2}$

$ \Rightarrow $${a^{x - 2}}{b^{y - 2}}{c^{z - 2}} = 1 = {a^0}{b^0}{c^0}$

$\therefore x = y = z = 2$

$\therefore xyz = {2^3} = 8 = x + y + z + 2$.

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