MHB How would you do this equation?

[Simon T]

1.05 = (1 + i)^6

 

[MarkFL]

Assuming $i$ is a variable, and not the imaginary unit, are you interested in all 6 roots, or just the reals, or just the positive reals?

 

[Simon T]

im not too sure what you mean. Here's a screenshot of the question:

 

[MarkFL]

Well, what does $i$ represent...an interest rate? If so, then we are only interested in the positive real root.

 

[Simon T]

it just says solve the power equation

 

[MarkFL]

Okay, well to get all 6 roots, I would let:

$$r=\sqrt[3]{\frac{21}{20}}$$

And write the equation as:

$$\left((1+i)^2\right)^3-r^3=0$$

Now, factor this as a difference of cubes...what do you get?