## amoodarya one year ago how do I solve this equation ?

1. amoodarya

$3\sin^3x+2\cos^3x=2sinx+cosx$

2. mathslover

I'll be more than fascinated to see what you've tried yet, amoodarya.

3. amoodarya

I need to solve it analytical ! not by graph , I know one of roots is $\frac{\pi}{3}$

4. mathslover

I wonder, were you given with that root or did you calculate it on your own?

5. amoodarya

I test it , but I can't solve it nice !

6. mathslover

One method is to follow the conventional way - that is putting $$\sin x = \sqrt{1- \cos^2 x}$$ Although, this is complicated. But, are you studying topic related to systems of equations (or similar to this) ...?

7. mathslover

And if one of the roots is $$\pi/3$$ then : $$3(3\sqrt{3} /8 ) + 2 (1/8) = 2(\qrt{3})/2 + 1/2 \\ 9\sqrt{3} /8 + 1/4 = \sqrt{3} + 1/2$$ This root doesn't seem to satisfy the given equation.

8. anonymous

At first sight, I can't see a nice solution to this problem, maybe Weierstrass substitution will work

9. amoodarya

i solve it numerically , then I saw one root is very close to pi/3 , but missed to check it in equation . thanks for your notification " mukushla"

10. anonymous

no problem amoodarya

11. ganeshie8