Let α, β, γ be three nonzero real numbers such that the equation √3α cos x+2β sin x=γ, x∈[−π2,π2] has two distinct real roots a and b with a+b=π3. If the range of values of 2γ3α+2β is [q,r), then the value of q+r is

Let α, β, γ be three nonzero real numbers such that the equation

1.	Let α, β, γ be three nonzero real numbers such that the equation √3α cos x+2β sin x=γ, x∈[−π2,π2] has two distinct real roots a and b with a+b=π3. If the range of values of 2γ3α+2β is [q,r), then the value of q+r is
Answer» Let $α, β, γ$ be three nonzero real numbers such that the equation $\sqrt{3} α cos x + 2 β sin x = γ, x \in [- \frac{π}{2}, \frac{π}{2}]$ has two distinct real roots $a$ and $b$ with $a + b = \frac{π}{3}$ . If the range of values of $\frac{2 γ}{3 α + 2 β}$ is $[q, r)$ , then the value of $q + r$ is