IGNOU MTE 11 2018 - Prove thatfor all m > 0, n > 0.Hence evaluate (10,7) and&nbs

Question

Prove that
$\beta (m,n) = \frac{\sqrt{m\sqrt{n}}}{\sqrt{m\sqrt{n}}}$
for all m > 0, n > 0.Hence evaluate $\beta$ (10,7) and $\beta(\frac{1}{2} ,\frac{1}{2})$ .

14 Feb 2018

Answer :

Word Count : 168

We are tasked with proving that: \[ \beta (m, n) = \frac{\sqrt{m\sqrt{n}}}{\sqrt{m\sqrt{n}}} \] for all $ m > 0 $ and $ n > 0 $, and then evaluating $\beta(10, 7)$ and $\beta\left(\frac{1}{2}, \frac{1}{2}\right)$. ### Step 1: Simplification of the Expression The given expression is: \[ \beta (m, n) = \frac{\sqrt{m\sqrt{n}}}{\sqrt{m\sqrt{n}}} \]

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