Question

If $x{y}^2=a^3,y{z}^2=b^3$ and $z{x}^2=c^3$ then $z^3$ equals

• A. $\frac{b{c}^4}{a^2}$
• B. $\frac{b^{4}c}{a^2}$
• C. $\frac{b^2{c}^4}{a^2}$
• D. $\frac{a{b}^4}{c^2}$

Answer 1

The correct option is B $\frac{b^{4}c}{a^2}$

$x{y}^2=a^3$ (1)

$y{z}^2=b^3$ (2)

$z{x}^2=c^3$ (3)

From (3) $z=\frac{c^3}{x^2}$ (4)

Substituting value of x from (1) in (4)

$z=\frac{c^3}{(\frac{a^3}{y^2}{)}^2}=\frac{c^3{y}^4}{a^6}$ (5)

Substituting value of y from (2) in (5)

$z=\frac{c^3(\frac{b^3}{z^2}{)}^4}{a^6}=\frac{c^3{b}^{12}}{z^8{a}^6}$ (6)

From (6)

$z^9=\frac{c^3{b}^{12}}{a^6}$

$z^3=\frac{c{b}^4}{a^2}$