1. ## Equation Solution

Good afternoon. I want some help in this exercise:

Solve in R the equation $4x\sin(\omega x) - x^2 - 4 = 0$

I have tried to convert it in a perfect square form but i came out with this $(x - 2 \sin(\omega x))^2 + 4 (\cos(\omega x))^2 = 0$ and i can't solve this. Can anyone help, please?

2. ## Re: Equation Solution

If your perfect square is rigth you're almost done if $x$ is real. Because you have the sum of two squared quantities equal to zero, both shall be zero.

Wolframalpha says solve 4&#42;x&#42;sin&#40;w&#42;x&#41;-x&#94;2-4&#61;0 - Wolfram|Alpha

3. ## Re: Equation Solution

Thanks, but i am not permitted to solve it with Wolfram. I must use algebra-trigonometry of High School. That's why I have stucked at the sum of perfect squares.

4. ## Re: Equation Solution

Originally Posted by ManosG
Good afternoon. I want some help in this exercise:

Solve in R the equation $4x\sin(\omega x) - x^2 - 4 = 0$

I have tried to convert it in a perfect square form but i came out with this $(x - 2 \sin(\omega x))^2 + 4 (\cos(\omega x))^2 = 0$ and i can't solve this. Can anyone help, please?
Where has this equation come from? I seriously doubt it could have come from high school, seeing as it's impossible to exactly solve equations that have the unknown both inside and outside of transcendental functions (unless you are very lucky and good at guessing).

5. ## Re: Equation Solution

Ok, thanks very much!