If (a^{x} = bc,b^{y} = ca,c^{z} = ab,) then (xyz) = | MATH - INDICES AND SURDS | SolveeIt

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

$x + y + z$

$x + y + z + 2$

Answer

$x + y + z + 2$

Explanation

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

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

$\therefore$ $x = y = z = 2$

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

Question: If \(a^{x} = bc,b^{y} = ca,c^{z} = ab,\) then \(xyz\) =...