Find the A.M. between: (x - y) and (x + y) - Vidyadip

Question

Find the A.M. between:
(x - y) and (x + y)

✓

Answer

(x - y) and (x + y)
Let A be the arithem atic mean of (x - y) and (x + y)
Then,
$(\text{x}-\text{y}),\ \text{A},\ (\text{x}+\text{y})$ are in A.P
$\Rightarrow\text{A}-(\text{x}-\text{y})=(\text{x}+\text{y})-\text{A}$
$\Rightarrow\text{A}=\frac{(\text{x}-\text{y})+(\text{x}+\text{y})}{2}=\frac{2\text{x}}{2}=\text{x}$
$\therefore$ A.M is x

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