Question : Find the value of $[49^{\frac{3}{2}}+49^{-\frac{3}{2}}]$.
Option 1: $\frac{11749}{343}$
Option 2: $\frac{117550}{343}$
Option 3: $\frac{117659}{343}$
Option 4: $\frac{117650}{343}$
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Correct Answer: $\frac{117650}{343}$
Solution : Given: $[49^{\frac{3}{2}}+49^{-\frac{3}{2}}]$ Simplifying this expression by factorising, we have, = $[(7^{2})^{\frac{3}{2}}+(7^{2})^{\frac{–3}{2}}]$ = $[7^{3}+7^{–3}]$ = $[343+\frac{1}{7^{3}}]$ = $[343+\frac{1}{343}]$ = $[\frac{117649+1}{343}]$ = $\frac{117650}{343}$ Hence, the correct answer is $\frac{117650}{343}$.
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