if a+1/a = 0 then √a+1/√a is equal to?
You asked:
Given \(a + \frac{1}{a} = 0\) evaluate the expression \(\sqrt{a} + \frac{1}{\sqrt{a}}\).
MathBot Answer:
\(\sqrt{a} + \frac{1}{\sqrt{a}} \in \left\{- i^{\frac{3}{2}} + \sqrt{i}, \sqrt{- i} + \frac{1}{\sqrt{- i}}\right\}\)
\(i\) is the imaginary unit, defined as \(i^2 = -1\).
By substituting this value into the expression, we find that: $$\begin{aligned}\sqrt{a} + \frac{1}{\sqrt{a}} &= \frac{1}{\sqrt{i}} + \sqrt{i}\\&= - i^{\frac{3}{2}} + \sqrt{i}\end{aligned}$$