Make $t$ the subject of the formula $s=a+\sqrt{\frac{ab}{t}+{{a}^{2}}}$. Hence, or otherwise, ca

Question

Make $t$ the subject of the formula $s=a+\sqrt{\frac{ab}{t}+{{a}^{2}}}$. Hence, or otherwise, calculate $t$ when $a=-\frac{3}{4}$, $b=-20$ and $s=-8$.

Accepted Answer

(a) $t=\frac{ab}{s^2-2as}$, subject to $s\ge a$ and $s^2-2as\ne0$ (b) No real value of $t$

Rearranging a Radical Formula to Make \(𝑡\) the Subject

Rearranging a Radical Formula to Make \(𝑡\) the Subject

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