The value of ${(7^{- 1} - 8^{- 1})}^{- 1} - {(3^{- 1} - 4^{- 1})}^{- 1}$ is

$44$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$56$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$68$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$12$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$44$

Explanation for the correct option:
Find the value of ${(7^{- 1} - 8^{- 1})}^{- 1} - {(3^{- 1} - 4^{- 1})}^{- 1}$
$\begin{array}{rcl} {(7^{- 1} - 8^{- 1})}^{- 1} - {(3^{- 1} - 4^{- 1})}^{- 1} & = & {(\frac{1}{7} - \frac{1}{8})}^{- 1} - {(\frac{1}{3} - \frac{1}{4})}^{- 1} [∵ a^{- m} = \frac{1}{a^{m}}] \\ = & {(\frac{8 - 7}{56})}^{- 1} - {(\frac{4 - 3}{12})}^{- 1} \\ = & {(\frac{1}{56})}^{- 1} - {(\frac{1}{12})}^{- 1} \\ = & 56 - 12 \\ = & 44 \\ ∴ {(7^{- 1} - 8^{- 1})}^{- 1} - {(3^{- 1} - 4^{- 1})}^{- 1} & = & 44 \end{array}$
Hence,the correct option is A

Suggest Corrections

Similar questions

{tan}^{- 1} \frac{1}{5} + {tan}^{- 1} \frac{1}{7} + {tan}^{- 1} \frac{1}{3} + {tan}^{- 1} \frac{1}{8} - \frac{π}{4}

\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}}

\frac{1}{\sqrt{9} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{1}}

= \frac{1}{3 - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - \sqrt{4}}

(\frac{1}{\sqrt{9} - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - \sqrt{4}})

Join BYJU'S Learning Program