Question

If a, b, c are in A.P., prove that:
(a — c)2 = 4 (a — b)(b — c)

Answer 1

Answer:

A, b, c are in A. P.

SO,

We can say that,

=> b - a = c - b

or, c +a = 2b

Squaring both sides

=-=-=-=-=-=-=-=-=-=-=-=

=> ( c +a) ² = (2b)²

or, (c - a) ² +4ac = 4b²

or, (c-a) ² = 4b² - 4ac

or, (c-a) ² = 4(b² - ac)

____<proved>______

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