Q65 / 160 · TS EAMCET 2020 (10 Sep Shift 2) · Mathematics

$\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})=$

  • A
    $\sinh ^{-1} 3+\cosh ^{-1}\left(\frac{1}{3}\right)$
  • Correct answer
    B
    $\cosh ^{-1} 3+\sinh ^{-1} 3$
  • C
    $\tanh ^{-1} 3+\sinh ^{-1} 3$
  • D
    $\cosh ^{-1} 3+\tanh ^{-1} 3$

Solution

We have, $\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})$ $\log (9+6 \sqrt{2}+3 \sqrt{10}+4 \sqrt{5})$ $\log (9+3 \sqrt{10}+6 \sqrt{2}+4 \sqrt{5})$ $\log (3+\sqrt{10})(3+2 \sqrt{2})$ $=\log (3+\sqrt{10})+\log (3+\sqrt{8})$ $=\log \left(3+\sqrt{3^2+1}\right)+\log \left(3+\sqrt{3^2-1}\right)$ $=\sin \mathrm{h}^{-1} 3+\cosh ^{-1} 3$

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

Relevant Questions