Question

Make r the subject of the formula (a/√r–b)²= c

Answer 1

$Given \: formula: \Big( \frac{a}{\sqrt{r-b)}}\Big)^{2} = c$

$\implies \Big( \frac{a}{\sqrt{r-b)}}\Big)=\pm \sqrt{ c }$

$\implies \frac{a}{\pm \sqrt{c}} = \sqrt{r-b}$

/* On squaring both sides,we get */

$\implies \Big( \frac{a}{\pm \sqrt{c}}\Big)^{2} = r - b$

$\implies \frac{a^{2}}{c} = r - b$

$\implies r - b = \frac{a^{2}}{c}$

$\implies r = \frac{a^{2}}{c} + b \: \blue { ( r \:is \: subject ) }$

Therefore.,

$\red{ r} \green { =\frac{a^{2}}{c} + b} \\ \blue { ( r \:is \: subject ) }$

•••♪

Answer 2

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ required \ formula \ is \ r=\frac{a^{2}}{c}+b}$

$\sf\orange{Given:}$

$\sf{\implies{(\frac{a}{\sqrt{r-b}})^{2}=c}}$

$\sf\pink{To \ find:}$

$\sf{Formula \ where \ r \ is \ the \ subject.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\implies{(\frac{a}{\sqrt{r-b}})^{2}=c}}$

$\sf{\implies{\frac{a^{2}}{r-b}=c}}$

$\sf{\implies{\frac{1}{r-b}=\frac{c}{a^{2}}}}$

$\sf{By \ Invertendo }$

$\sf{\implies{r-b=\frac{a^{2}}{c}}}$

$\sf{\implies{r=\frac{a^{2}}{c}+b}}$

$\sf{Here, \ r \ is \ the \ subject.}$

$\sf\purple{\tt{\therefore{The \ required \ formula \ is \ r=\frac{a^{2}}{c}+b}}}$