a-xy-x-y-b-xz-x-z-and-c-yz-y-z-Represent-x-in-a-b-c-form-x-y-z-0-

Question Number 191595 by MATHEMATICSAM last updated on 26/Apr/23

a = \frac{x y}{x + y}, b = \frac{x z}{x + z} and c = \frac{y z}{y + z} .

Represent x in a, b, c form . [x, y, z \neq 0]

Answered by mehdee42 last updated on 26/Apr/23

\frac{1}{a} = \frac{1}{x} + \frac{1}{y} (i), \frac{1}{b} = \frac{1}{x} + \frac{1}{z} (i i), \frac{1}{c} = \frac{1}{y} + \frac{1}{z} (i i i)

(i), (i i) \Rightarrow \frac{1}{a} + \frac{1}{b} = \frac{2}{x} + \frac{1}{y} + \frac{1}{z} \overset{(i i i)}{\Rightarrow} \frac{1}{a} + \frac{1}{b} = \frac{2}{x} + \frac{1}{c}

\Rightarrow x = \frac{a c + b c - a b}{2 a b c} ✓

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