Solve #x^2-9 = tanx # ?

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Answer 1 · 2018-01-03T17:29:14

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

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:

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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#