Q51 / 170 · Manipal (MET) 2021 · Mathematics

$\frac{5^{\frac{3}{2}}-2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}}+\frac{5^{\frac{3}{2}}+2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}}$

  • A
    7
  • Correct answer
    B
    14
  • C
    12
  • D
    8

Solution

Now, $\begin{aligned} & \frac{5^{\frac{3}{2}}-2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}}+\frac{5^{\frac{3}{2}}+2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}} \\ = & \frac{\sqrt{5}^3-\sqrt{2}^3}{\sqrt{5}-\sqrt{2}}+\frac{\sqrt{5}^3+\sqrt{2}^3}{\sqrt{5}+\sqrt{2}} \\ = & (5+2+\sqrt{10})+(5+2-\sqrt{10}) \\ = & 7+7=14\end{aligned}$

Hence, the correct answer is option: 'B'.

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