Question

7m² – 84 = 8

Answer 1

Given: 7m² – 84 = 8

The equation can be rewritten as:

7m² – 84 – 8 = 0

$\Rightarrow$7m² – 92 = 0

$\Rightarrow$m² – $\frac{92}{7}$ = 0

$\Rightarrow$m² – ${\left(\sqrt{\frac{92}{7}}\right)}^2$ = 0

$\Rightarrow m^2-{\left(2\sqrt{\frac{23}{7}}\right)}^2=0$

On using the identity (a² – b²) = (a + b)(a – b), we get:

$\left(m+2\sqrt{\frac{23}{7}}\right)\left(m-2\sqrt{\frac{23}{7}}\right)=0$

We know that if the product of two numbers is zero, then at least one of them must be zero.

Thus,
$$\begin{gathered} m+2\sqrt{\frac{23}{7}}=0\mathrm{or}\mathrm{m}-2\sqrt{\frac{23}{7}}=0 \\ \Rightarrow \mathrm{m}=-2\sqrt{\frac{23}{7}}\mathrm{or}\mathrm{m}=2\sqrt{\frac{23}{7}} \end{gathered}$$

Therefore, the solution of the given equation is $\pm 2\sqrt{\frac{23}{7}}$.