If-a-x-px-a-y-qy-a-z-rz-and-p-q-r-are-in-AP-then-x-y-z-will-be-in-

Question Number 46924 by 786786AM last updated on 02/Nov/18

If \frac{a - x}{p x} = \frac{a - y}{q y} = \frac{a - z}{r z} and p, q, r are

in AP, then x, y, z will be in

Answered by tanmay.chaudhury50@gmail.com last updated on 02/Nov/18

\frac{a - x}{p x} = \frac{a - y}{q y} = \frac{a - z}{r z} = \frac{1}{k} (s a y)

p x = k (a - x)

p = \frac{k (a - x)}{x}

q == \frac{k (a - y)}{y}

r = \frac{k (a - z)}{z}

2 q = p + r

\frac{2 k (a - y)}{y} = \frac{k (a - x)}{x} + \frac{k (a - z)}{z}

\frac{2 (a - y)}{y} = \frac{a - x}{x} + \frac{a - z}{z}

\frac{2 a}{y} - 2 = \frac{a}{x} - 1 + \frac{a}{z} - 1

\frac{2}{y} = \frac{1}{x} + \frac{1}{z} s o x, y, z a r e i n H P