Question

I need help with solving this equation?

`3/m^2=1/2m^2+2/m`

Answer 1

`m=-1.92371...`

`m=1.11441...`

Explanation:

.

`3/m^2=1/2m^2+2/m`

Let's multiply both side by `2m^2`:

`6=m^4+4m`

`m^4+4m-6=0`

Since this is an equation of degree `4`, you have to either use a graphing utility to solve it or use the Newton-Raphson method.

But as this problem was posted as an algebra problem, I am going to assume you have not yet taken calculus which is where the latter method is typically learned.

Please see the graph of this function below:

As you can see, the graph crosses the `x`-axis at two points:

`m~=-2` and `m~=1`

Now, to get more exact answers, you can try values close to these roots on both sides of each. Using this iterative process, you can get closer and closer to the actual values of `m`.

You will find that they are:

`m=-1.92371...`

`m=1.11441...`