Giải các phương trình:
$a)   \sin^62x+\cos^62x=\dfrac{3}{2}\left(\sin^42x+\cos^42x\right)+\dfrac{1}{2}\left(\sin x+\cos x\right)$
$b)   3\sin4x=\left(\cos2x-1\right)\tan x$
$c)    \left(1+\cos x\right)\sqrt{\tan\dfrac{x}{2}}-2+\sin x=2\cos x$

nhìn khủng thế –  kellyhoang297 07-11-12 09:21 PM
nhìn hoa cả mắt –  yeuhoahocneu 07-11-12 08:52 PM
nhìn hơi cồng kềnh nhưng giải cũng không khó lắm –  cuungonghinh 07-11-12 08:19 PM
a) PT đã cho tương đương với:
$2(\sin ^22x+\cos ^22x)(\sin ^42x-\sin ^22x\cos ^22x+\cos ^42x)=3(\sin ^42x+\cos ^42x)+\sin x+\cos x$.
$\Leftrightarrow \sin ^42x+2\sin ^22x\cos ^22x+\cos ^42x+\sin x+\cos x=0.$
$\Leftrightarrow (\sin ^22x+\cos ^22x)^2+\sin x+\cos x=0.$
$\Leftrightarrow \sin x+\cos x=-1.$
$\Leftrightarrow x=-\frac{\pi}{2}+k2\pi \vee x=\pi+k2\pi,k\in Z$.

b) ĐK: $x\neq \frac{\pi}{2}+k\pi$. PT đã cho tương đương với:
$6\sin 2x\cos 2x=-2\sin^2x.\frac{\sin x}{\cos x}.$
$\Rightarrow 6\sin x\cos ^2x\cos 2x+\sin ^3x=0$.
$\Leftrightarrow \sin x(3\cos 2x+1)(2\cos 2x+1)=0$.
Nếu $\sin x=0$ thì $x=k\pi,k\in Z$.
Nếu $3\cos 2x+1=0$ thì $x=\pm \frac{\alpha}{2}+k\pi,k\in Z$ trong đó $\alpha \in (0,\pi)$ thỏa mãn $\cos \alpha =\frac{-1}{3}$.
Nếu $2\cos 2x+1=0$ thì $x=\pm \frac{\pi}{3}+k\pi,k\in Z$.

c) ĐK: $2k\pi \leq x<(2k+1)\pi,k\in Z.$ Khi đó đặt $\tan \frac{x}{2}=t\geq 0$ thì PT đã cho trở thành:
\[ \left( 1+\frac{1-t^4}{1+t^4}\right) t-2+\frac{2t^2}{1+t^4}=2.\frac{1-t^4}{1+t^4}.\]
\[ \Leftrightarrow (t+1)(2t^3-2t^2-t+2)=0 \]
Với $t\geq 0$ thì $2t^3-2t^2-t+2=2(t-1)^2(t+1)+t>0$ nên PT trên vô nghiệm, suy ra PT đã cho vô nghiệm.
ad giải chi tiết nhờ –  duachua.no1 07-11-12 10:47 PM
oai, nhìn đề khó kinh –  duachua.no1 07-11-12 10:47 PM
ad giải cũng dễ hiểu –  yeuhoahocneu 07-11-12 08:52 PM
hay nhờ keomut ơi –  luffykunneu 07-11-12 08:08 PM
lời giải hay nhỉ –  banhquykeomut 07-11-12 08:05 PM

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