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if (1/x) + (1/x-a) + (1/x-b)=0. prove that one root lies between a/3 and 2a/3 , and other lies between b/3 and 2b/3 PLS HELP WITH EXPLANATION..ANSWER WILL SURELY BE APPROVED!!


if (1/x) + (1/x-a) + (1/x-b)=0.


prove that one root lies between a/3 and 2a/3 , and other lies between b/3 and 2b/3 


 


PLS HELP WITH EXPLANATION..ANSWER WILL SURELY BE APPROVED!!


Grade:9

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

\frac{1}{x} + \frac{1}{x-a} + \frac{1}{x-b} = 0
\frac{1}{x-a} + \frac{1}{x-b} = \frac{-1}{x}
x(2x-a-b) = -(x^{2}-(a+b)x+ab)
3x^2 - 2(a+b)x+ab = 0
x = \frac{2(a+b)\pm \sqrt{4(a+b)^2-12ab}}{6}
x = \frac{(a+b)\pm \sqrt{(a+b)^2-3ab}}{3}
From here it is clear that one root lie b/w a/3 & 2a/3 and other b/w b/3 & 2b/3.

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