InterviewSolution
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InterviewSolution
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\(\sqrt{\cfrac{a}{b}+\cfrac{b}{a}-2}\) = ..............√(a/b + b/a - 2)A) \(\sqrt{\cfrac{a}{b}}\) - \(\sqrt{\cfrac{b}{a}}\)B) \(\sqrt{\cfrac{a}{b}}\) + \(\sqrt{\cfrac{b}{a}}\)C) \(\cfrac{a}{\sqrt{b}}\) + \(\cfrac{b}{\sqrt{a}}\)D) \(\cfrac{a}{b}\) + \(\cfrac{b}{a}\) |
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Answer» Correct option is (A) \(\sqrt\frac{a}{b}-\sqrt\frac{b}{a}\) \(\sqrt{\frac{a}{b}+\frac{b}{a}-2} \) \(=\sqrt{\left(\sqrt{\frac ab}\right)^2+\left(\sqrt{\frac ba}\right)^2-2\sqrt{\frac ab}\times\sqrt{\frac ba}} \) \(=\sqrt{\left(\sqrt{\frac ab}-\sqrt{\frac ba}\right)^2} \) (By assuming \(\sqrt\frac{a}{b}=A\,\&\,\sqrt\frac{b}{a}=B\) and \((A-B)^2=A^2+B^2-2AB)\) \(=\left(\left(\sqrt{\frac ab}-\sqrt{\frac ba}\right)^2\right)^\frac12\) \(=\sqrt\frac{a}{b}-\sqrt\frac{b}{a}\) Correct option is A) \(\sqrt{\cfrac{a}{b}}\) - \(\sqrt{\cfrac{b}{a}}\) |
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