True / False

Say true or false. The A.M. between $$(a-b)^2$$ and $$(a+b)^2$$ is $$a^2+b^2 $$.

ATRUE
Correct Answer
BFALSE

Solution

If the two terms are $$x$$ and $$y$$, then their AM is $$\dfrac{x+y}{2}$$
AM between $$(a-b)^2$$ and $$(a+b)^2$$
$$=$$ $$\dfrac{(a-b)^2 + (a+b)^2}{2}$$
$$=$$ $$\dfrac{(a^2 +b^2 - 2ab + a^2+b^2 + 2ab)}{2}$$
$$=$$ $$a^2 + b^2$$

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