InterviewSolution
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InterviewSolution
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A rationalising factor of \(^3\sqrt{25}\) + \(\cfrac{1}{^3\sqrt{25}}\) - 1 is ...................(A) 51/3 - 51/3(B) 51/3 + 51/3(C) 251/3 + 25-1/3(D) 251/3 - 25-1/3 |
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Answer» Correct option is (B) 51/3 + 51/3 \(\because\left((25)^\frac13+\frac1{(25)^\frac13}-1\right)\left(5^\frac13+\frac1{5^\frac13}\right)\) \(=\left(5^\frac23+\frac1{5^\frac23}-1\right)\left(5^\frac13+\frac1{5^\frac13}\right)\) \(=5^\frac23.5^\frac13+\cfrac{5^\frac13}{5^\frac23}-5^\frac13+\cfrac{5^\frac23}{5^\frac13}+\frac1{5^\frac23\,5^\frac13}-\frac1{5^\frac13}\) \(=5^\frac33+\frac1{5^\frac13}-5^\frac13+5^\frac13+\frac1{5^\frac33}-\frac1{5^\frac13}\) \((\because a^m.a^n=a^{m+n}\,and\,\cfrac{a^m}{a^n}=a^{m-n})\) \(=5+\frac15=\frac{26}5\) which is a rational number. Thus, \((5^{\frac{1}{3}}+\frac1{5^{\frac{1}{3}}})\) is a rationalising factor of \((25^\frac13+\frac1{25^\frac13}-1).\) Correct option is (B) 51/3 + 51/3 |
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