22.
\(\Leftrightarrow3x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+k\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{6}+\dfrac{k\pi}{3}\)
\(0\le-\dfrac{\pi}{6}+\dfrac{k\pi}{3}\le\dfrac{3\pi}{2}\Rightarrow k=\left\{1;2;3;4;5\right\}\)
Vậy pt có 5 nghiệm trên đoạn đã cho là:
\(x=\left\{\dfrac{\pi}{6};\dfrac{\pi}{2};\dfrac{5\pi}{6};\dfrac{7\pi}{6};\dfrac{3\pi}{2}\right\}\)
23.
\(\Leftrightarrow2x-\dfrac{\pi}{4}=\dfrac{\pi}{6}+k\pi\)
\(\Leftrightarrow x=\dfrac{5\pi}{24}+\dfrac{k\pi}{2}\)
\(\dfrac{\pi}{2}\le\dfrac{5\pi}{24}+\dfrac{k\pi}{2}\le\dfrac{5\pi}{2}\) \(\Rightarrow k=\left\{1;2;3;4\right\}\)
Vậy pt có 4 nghiệm trên đoạn đã cho là:
\(x=\left\{\dfrac{17\pi}{24};\dfrac{29\pi}{24};\dfrac{41\pi}{24};\dfrac{53\pi}{24}\right\}\)
