Show-that-the-equation-1-x-a-1-x-b-1-x-c-0-can-have-a-pair-of-equal-roots-if-a-b-c-

Question Number 20013 by Tinkutara last updated on 20/Aug/17

Show that the equation \frac{1}{x - a} + \frac{1}{x - b}

+ \frac{1}{x - c} = 0 can have a pair of equal

roots if a = b = c .

Commented by ajfour last updated on 20/Aug/17

h o w d i d u s o l v e i t, p l e a s e l e t m e

k n o w .

Commented by ajfour last updated on 20/Aug/17

i f a = b = c = k

f (x) = \frac{3}{x - k} n o r o o t s!

Commented by ajfour last updated on 20/Aug/17

t h a n k s .

Commented by Tinkutara last updated on 20/Aug/17

\frac{1}{x - a} + \frac{1}{x - b} = \frac{1}{c - x}

\frac{2 x - a - b}{(x - a) (x - b)} = \frac{1}{c - x}

A quadratic equation can be formed by

more simplification, and then we have

to put discriminant = 0 and then we

will get {(a - b)}^{2} + {(b - c)}^{2} + {(c - a)}^{2} = 0

\Rightarrow a = b = c .