Solve this Equation?

Question

tan 3x = (3t - t^3)/(t - 3t^2)

where t = tan x

Solve this equation
4t^3 + 3t^2 - 12t - 1 = 0

The answers are -2.11, -0.0818, 1.45. Could someone who knows the correct method to solve this show how its done? I got -0.0818 but could not get the rest.

Answer 1

These are called 'transcendental' equations. Trig functions are transcendental functions. There's not general method for solving such equations. That makes them fun because you have to be creative.

Note that the algebraic equation is 3rd order with a positive coefficient on the high order term. This means that it's range is - inf to + inf. It can have a maximum of 3 real zeros. Tax x has period pi and so it is zero at zero and integer multiples of pi. If you have a graphics calculator you might consider getting a graphical solution.

I hope that this helps. If you post again then I'll take the trouble of breaking out my TI-83 and give it a go.

Answer 2

the answer is nineteen! unique how-to under: to make this greater trouble-free, team the x's inclusive of, of course, their +/- signs and indicators: 3x - 2x + 17 + 2 now it rather is an equation, and in case you notice no equivalent sign (=), then you quite ought to assume that if there replaced into, your finished equation must be equivalent to 0: 3x - 2x + 17 + 2 = 0 now simplify-- use easy subtraction while dealing with the variables (ignoring the x's, yet remembering to place them interior the effect) this implies which you ought to respond to "3-2": 1x + 19 = 0 i've got been given the nineteen by potential of including 17 and a pair of. you at the instant have a "1x", yet you will get rid of the "a million", through fact writing down merely "x" rather potential "1x" x + 19 = 0 now to unravel it, the variable must be on one facet, and the standard fee on the different facet. bear in mind that in case you're taking a huge determination or a variable around the equivalent sign, you will be able to desire to constantly substitute it quite is +/- sign! : x = -19 or 19 = -x now you have the answer! x is comparable to "damaging 19" or "-19" or you are able to study it as "damaging x is comparable to 19", that's the comparable element. desire this replaced into sufficient element.

Answer 3

if the solutions are a, b, c then

a+b+c=-3/4
ab+bc+ca=-3
abc=1/4

solve these eqns and u'll get ur results.

Answer 4

ask albert