Question

If $s=t+\sqrt{\frac{r^3}{q}}$, then find the value of $r$ in terms of $q,s$ and $t$.

• A. $\sqrt[3]{3q{s}^2-qt}$
• B. $\sqrt[3]{3\frac{s^2-2st-t^2}{q}}$
• C. $\sqrt[3]{3q{s}^2-2qst+q{t}^2}$
• D. $\sqrt{\frac{q{s}^2+2qst-t^2}{3}}$
• E. $\frac{q{s}^2-2st+t^2}{3}$

Answer 1

The correct option is C $\sqrt[3]{3q{s}^2-2qst+q{t}^2}$

Given, $s=t+\sqrt{\frac{r^3}{q}}$
$\sqrt{\frac{r^3}{q}}=s-t$
$\frac{r^3}{q}={(s-t)}^2$
$r^3=q{(s-t)}^2$
$r=\sqrt[3]{3q{(s-t)}^2}=\sqrt[3]{3q{s}^2-2qst+q{t}^2}$