Question

1 - 2sin\(^2\)x.cos\(^2\)x + \(\dfrac{1}{2}\)cos\(^2\)2x = 0

Answer 1

\(1-2sin^2x.cos^2x+\dfrac{1}{2}cos^22x=0\)

\(\Leftrightarrow1-\dfrac{1}{2}sin^22x+\dfrac{1}{2}cos^22x=0\)

\(\Leftrightarrow1+\dfrac{1}{2}cos4x=0\)

\(\Leftrightarrow cos4x=-2\)

\(\Rightarrow\) phương trình vô nghiệm.

Answer 2

Lời giải:
PT $\Leftrightarrow 2-4\sin ^2x\cos ^2x+\cos ^22x=0$

$\Leftrightarrow 2-(\sin 2x)^2+\cos ^22x=0$

$\Leftrightarrow 2+\cos 4x=0$

$\Leftrightarrow \cos 4x=-2< -1$ (vô lý)

Vậy pt vô nghiệm