Question

Solve `x^2-9 = tanx` ?

Answer 1

`color(red)(x approx { -4.784 , -3.02 , -1.428 , 1.736 , 2.971 , 4.632 }`

Explanation:

There are a few ways that i can think of:

Graphically...

We notice that the solutions of this particular equation is where the functions `y = x^2 - 9` and `y = tanx` Intersect

Were i am assuming you understand radians...

Hence graphing:

We can make out the approximate solitions for `x`:

`color(red)(x approx { -4.784 , -3.02 , -1.428 , 1.736 , 2.971 , 4.632 }`

The other way i can breifly describe is a method called Newton- Raphson...

Where you can solve `f(x) = 0` by the follwoing:

`x_(n+1) = x_n - (f(x_n) )/ (f'(x_n) )`

Where `x_n` is an approximate solution and `x_(n+1)` is typically a more acurate approximation...

So we can use this with `x^2 - 9 - tanx = 0`

for more info about newton-raphson methods:
`->`http://personal.maths.surrey.ac.uk/st/S.Gourley/NewtonRaphson.pdf