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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

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello Student,
Please find answer to your question below
[{1}/{x} +{1}/{x-a} +{1}/{x-b} = 0]
[{1}/{x-a} {1}/{x-b} ={-1}/{x}]
[x(2x-a-b) = -(x^{2}-(a+b)x+ab)]
[3x^2 - 2(a+b)x+ab = 0]
[x = {2(a+b)\pmsqrt{4(a+b)^2-12ab}}/{6}]
[x = {(a+b)\pmsqrt{(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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