Find th sum of roots of 1-x-1-x-a-1-b-1-b-a a- 0

The correct option is A aGiven, 1 x 1 x a = 1 b 1 b a #160; = gt; x a x x(x a) = b a b b(b a) #160; = gt; a x(x a) = ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

Find th sum o...

Question

Find th sum of roots of $\frac{1}{x} - \frac{1}{x - a} = \frac{1}{b} - \frac{1}{b - a} (a \neq 0)$

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a - b

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a + b

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Solution

The correct option is A a
Given, $\frac{1}{x} - \frac{1}{x - a} = \frac{1}{b} - \frac{1}{b - a}$
$=> \frac{x - a - x}{x (x - a)} = \frac{b - a - b}{b (b - a)}$
$=> \frac{a}{x (x - a)} = \frac{a}{b (b - a)}$
$=> \frac{1}{x (x - a)} = \frac{1}{b (b - a)}$
$=> x (x - a) = b (b - a)$
$=> x^{2} - a x + (a b - b^{2}) = 0$

Sum of roots $= - \frac{C o e f f o f x}{C o e f f o f x^{2}} = - \frac{- a}{1} = a$

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