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Q.
The geometric and harmonic means of two positive numbers $x_1$ and $x_2$ are 18 and $16 \frac{8}{13}$ respectively. The value of $\left|x_1-x_2\right|$ is equal to
Sequences and Series
Solution:
$\Theta x _1 x _2=324 $
$\text { and } \frac{2 x _1 x _2}{ x _1+ x _2}=\frac{216}{13} \Rightarrow x _1+ x _2=39 $
$\Theta\left(x_1-x_2\right)^2=\left(x_1+x_2\right)^2-4 x_1 x_2=(39)^2-4 \times 324=225 $
$\Rightarrow\left|x_1-x_2\right|=15 . $