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The sum of a number and its reciprocal is 13/6 What is the number ? |
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Answer» Let number = x, then its reciprocal = 1/x \(x+\frac{1}{x}=\frac{13}{6},(x^2+1)\times6=13x\) 6x2 - 13x + 6 = 0 \(x=\frac{13\pm \sqrt{(-13)^2-4\times6\times6}}{2\times6}\) = \(\frac{13\pm \sqrt{169-144}}{12}=\frac{13\pm \sqrt{25}}{12}\) Number = \(\frac{3}{2}\) or \(\frac{2}{3}\) |
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