Solve the given quadratic equation by factorisation method, $m - \frac{7}{m} = 6$

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Solution

The given equation $m - \frac{7}{m} = 6$ can be simplified as follows:

$m - \frac{7}{m} = 6 \Rightarrow m^{2} - 7 = 6 m \Rightarrow m^{2} - 6 m - 7 = 0$

Now, the quadratic equation $m^{2} - 6 m - 7 = 0$ can be factorised as shown below:

$m^{2} - 6 m - 7 = 0 \Rightarrow m^{2} + m - 7 m - 7 = 0 \Rightarrow m (m + 1) - 7 (m + 1) = 0 \Rightarrow (m - 7) = 0, (m + 1) = 0 \Rightarrow m = 7, m = - 1$

Hence, $m = - 1$ or $m = 7$ .

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