Question

If $m+\frac{1}{m} =7$, find the value of $m^{3} +\frac{1}{m^3}$....

Answer 1

$m + \frac{1}{ m} = 7 \\ \\ {m}^{3} + \frac{1}{m {}^{3} } = ? \\ \\{m}^{3} + \frac{1}{m {}^{3} } = (m + \frac{1}{m} ) {}^{3} - 3.m. \frac{1}{m} (m + \frac{1}{m} ) \\ \\ = (7) {}^{3} - 3 \times 7 \\ \\ = 343 - 21 \\ \\ = 322$

I hope this helps.