Question

If a is the arithmetic mean between A and B, prove that (a−A)²=1/2​(A−B)².

(a) (a−A)²=1/2​(A−B)²
(b) (a−A)²=2(A−B)²
(c) (a−A)²=(A−B)²
(d) (a−A)²=−1/2​(A−B)²

Answer 1

To prove the equation (a - A)² = 1/2(A - B)², substitute the value of a as the mean between A and B and simplify the equation.

Step-by-step explanation:

To prove that (a-A)² = 1/2(A-B)², we need to show that both sides of the equation are equal.

We start with the fact that a is the arithmetic mean between A and B. This means that a = (A + B)/2.

Now, let's substitute this value of a in the equation:

(a - A)² = ([(A + B)/2] - A)²

= (B - A)/2)²

= 1/2(A - B)²

Therefore, the equation (a - A)² = 1/2(A - B)² is proven to be true.