Solve x^2-9 = tanx x29=tanx ?

1 Answer
Jan 3, 2018

color(red)(x approx { -4.784 , -3.02 , -1.428 , 1.736 , 2.971 , 4.632 } x{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 y=x29 and y = tanx y=tanx Intersect

Were i am assuming you understand radians...

Hence graphing:

enter image source here

We can make out the approximate solitions for xx:

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