Bài 2 : tan x = 3 \(\Rightarrow cotx=\dfrac{1}{3}\)

\(1+tan^2x=\dfrac{1}{cos^2x}\Rightarrow1+9=\dfrac{1}{cos^2x}\)  \(\Rightarrow cosx=\pm\dfrac{1}{\sqrt{10}}\)

cos x = \(\pm\dfrac{1}{\sqrt{10}}\Rightarrow sinx=\pm\dfrac{3}{\sqrt{10}}\)

\(...=\dfrac{2^{11}\left(1+2^4\right)}{1+2^4}=2^{11}\)

ĐKXĐ : \(x\ne\dfrac{\pi}{2}+k\pi\left(k\in Z\right)\)

... \(\Leftrightarrow\)\(sin^2x\left(tanx+1\right)=3\left[sinx.cosx-sin^2x+sin^2x+cos^2x\right]\)

\(\Leftrightarrow sin^2x.\dfrac{sinx+cosx}{cosx}=3cosx\left[sinx+cosx\right]\)

\(\Leftrightarrow\left(sinx+cosx\right)\left[\dfrac{sin^2x}{cosx}-3cosx\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx+cosx=0\left(1\right)\\sin^2x=3cos^2x\left(2\right)\end{matrix}\right.\)

(1) \(\Leftrightarrow\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)=0\) \(\Leftrightarrow...\)

(2) \(\Leftrightarrow1=4cos^2x\Leftrightarrow...\)

ĐKXĐ : \(x\ge0\)

A) ... = \(\dfrac{11}{68}-27,75+\dfrac{3}{34}\)  = \(\dfrac{1}{4}-27,75=-27,5\)

B) ... = \(0,3+1+1+1,7=4\)

\(...\Rightarrow3^n=81=3^4\Rightarrow n=4\)

\(Q=...=-1\left[x+y+xy+1\right]=-1\left[-1+2+1\right]=-1.2=-2\)

\(...=\left(x+y\right)^2-2\left(x+y\right)=\left(x+y\right)\left(x+y-2\right)\)

... = \(\dfrac{\sqrt{2}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\sqrt{4-4\sqrt{2}+2}\)  = \(\sqrt{2}+\sqrt{\left(2-\sqrt{2}\right)^2}=\sqrt{2}+2-\sqrt{2}=2\)

ĐKXĐ : \(x\ge-1\)

P/t \(\Leftrightarrow\left(2x^2-16x\right)-5\left(x-8\right)-5\left(x-2\right)\left[\sqrt{x+1}-3\right]=0\)

\(\Leftrightarrow2x\left(x-8\right)-5\left(x-8\right)-5\left(x-2\right)\dfrac{x-8}{\sqrt{x+1}+3}=0\)

\(\Leftrightarrow\left(x-8\right)\left[2x-5-\dfrac{5\left(x-2\right)}{\sqrt{x+1}+3}\right]=0\)

x = 8 là no của p/t

Xét [...]  \(\Leftrightarrow\left(2x-5\right)\left[\sqrt{x+1}+3\right]-5\left(x-2\right)=0\)

\(\Leftrightarrow\left(2x+2\right)\sqrt{x+1}+\left(\sqrt{x+1}-\dfrac{7}{2}\right)^2=\dfrac{73}{4}\)

Đặt a = \(\sqrt{x+1}\ge0\)  ; p/t \(\Leftrightarrow2a^3+\left(a-\dfrac{7}{2}\right)^2=\dfrac{73}{4}\)

\(\Leftrightarrow2a^3+a^2-7a-6=0\)  \(\Leftrightarrow\left(a-2\right)\left(a+1\right)\left(a+\dfrac{3}{2}\right)=0\)

\(\Leftrightarrow a=2\)  hay \(\sqrt{x+1}=2\Leftrightarrow x=3\)

Vậy p/t có 2 no x = 3 và x = 8