Question

How to solve this ?

Answer 1

`x=1.8557,2.6117,4.9973,5.7533`

Explanation:

`tan^2x+4tanx+2=0` can be solved using binomial formula

`tanx=(-4+-sqrt(4^2-4*1*2))/2=(-4+-sqrt8)/2=-2+-sqrt2`

i.e. either `tanx=-2+sqrt2=-2+1.4142=-0.5858`

i.e. `x=-0.53` and in `[0,2pi}` `x=3.1416-0.53=2.6117` or `x=2.6117+3.1416=5.7533`

and if `x=-2-sqrt2=-3.4142`, `x=-1.2859` ans in `[0,2pi)`

`x=3.1416-1.2859=1.8557` or `x=3.1416+1.8557=4.9973`