Question

m-1/m=2 then the value of m+1/m is ?

Answer 1

Answer:

The value of $m+\frac{1}{m}$ is (-2.83, 2.83).

Step-by-step explanation:

The provided expression is: $m-\frac{1}{m}=2$

Solve this for the values of m a follows:

$m-\frac{1}{m}=2\\\\m^{2}-1=2m\\m^{2}-2m-1=0$

The resultant equation is a quadratic equation.

The roots of a quadratic equation are:$\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}$

Here a = 1, b = -2 and c = -1.

The value of m are:

$m=\frac{-(-2)\pm\sqrt{(-2)^{2}-(4\times1\times-1)} }{2\times1}\\=\frac{2\pm\sqrt{8} }{2}\\ =\frac{2\pm2\sqrt{2} }{2}\\ =1\pm\sqrt{2}\\ =(-0.414, 2.414)$

• If m = -0.414 the value of $m+\frac{1}{m}$ is:

         $m+\frac{1}{m}=-0.414+\frac{1}{-0.414} =\frac{(-0.414)^{2}+1}{-0.414} =-2.83$

• If m = 2.414 the value of $m+\frac{1}{m}$ is:

          $m+\frac{1}{m}=2.414+\frac{1}{2.414} =\frac{(2.414)^{2}+1}{2.414} =2.83$

Thus, the value of $m+\frac{1}{m}$ is (-2.83, 2.83).