InterviewSolution
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InterviewSolution
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What are the roots of the equation (a + b + x)–1 = a–1 + b–1 + x–1 ? |
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Answer» Given, \(\frac{1}{a+b+x}\) = \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{x}\) ⇒ \(\frac{1}{a+b+x}\)- \(\frac{1}{x}\) = \(\frac{1}{a}\) + \(\frac{1}{b}\) ⇒ \(\frac{x-(a+b+x)}{x(a+b+x)}\) = \(\frac{a+b}{ab}\) ⇒ \(\frac{-(a+b)}{x(a+b+x)}\) = \(\frac{a+b}{ab}\) ⇒ – ab = x2 + (a + b)\(x\) ⇒ x2 + (a + b)\(x\) + ab = 0 ⇒ (\(x\) + a) (\(x\) + b) = 0 ⇒ \(x\) = – a, – b. |
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