Question

a*b=54,b*c=72,a*c=48,then a*b*c=?

Answer 1

$\textbf{Answer}$

$\textbf{We are given that,}$

a*b=54
b*c=72
a*c=48

$\textbf{Lets divide a*b=54 by b*c=72}$
(a*b)/(b*c) = 54/72
=> a/c = 3/4
=> a = 3c/4

$\textbf{Lets put a = 3c/4}$ in $\textbf{a*c = 48}$
a*c = 48
=> (3c/4)*c = 48
=> (c^2) = (48*4)/3
=> c^2 = 64
=> c = + 8 or -8

$\textbf{If c = 8,}$
=> a*c = 48
=> a = 48/8 = 6
=> b*c = 72
=> b = 72/8 = 9
=> a*b*c = 6×9×8
=> $\textbf{a*b*c = 432}$

$\textbf{If c = - 8,}$
a*c = 48
=> a = 48/-8
=> a = - 6
=> b*c = 72
=> b = 72/-8
=> b = - 9
=> a*b*c = (-6)*(-9)*(-8)
=> $\textbf{a*b*c = - 432}$

$\textbf{a*b*c = +432 or -432}$

$\textbf{Hope My Answer Helped}$
$\textbf{Thanks}$

Answer 2

a * b = 54 , b * c = 72,  a * c = 48

on multiply both side we get

a * b * b * c * c * a  = 54 * 72 * 48 

(abc)² = 186624

(abc) = √186624

HENCE, (abc) = +- 432