Question

Find the mean proportional between $4\frac{4}{7},3\frac{1}{2}$

Answer 1

If we have three numbers $a,b,c$ such that

$a:b=b:c$

Then $b$ is the mean proportion of $a$ and $c$

So, $b^2=ac$

here, $a=4\frac{4}{7}=\frac{32}{7}$

$c=3\frac{1}{2}=\frac{7}{2}$

Hence $b^2=\frac{32}{7}\times \frac{7}{2}$

$⟹b=\pm 4$

Thus, mean proportional is $4$