\(B=...=\left(a^4-2a^3+a^2\right)+\left(a^2-2a+1\right)+4\)  

= \(\left(a^2-a\right)^2+\left(a-1\right)^2+4\ge4>0\forall a\)  (đpcm) 

a) ... = \(\dfrac{1-cos^2\alpha-sin^2\alpha}{sin\alpha\left(1+cos\alpha\right)}=\dfrac{1-1}{...}=0\)

b) ... = \(tan^2\alpha\left(1-sin^2\alpha\right)-sin^2\alpha\)  = \(tan^2\alpha.cos^2\alpha-sin^2\alpha=sin^2\alpha-sin^2\alpha=0\)

d) \(4x^3-3x^2+2x-1=\left(4x^2+9x+29\right)\left(x-3\right)+86\)

e) \(\left(27x^3+125\right)=\left(9x^2-15+25\right)\left(3x+5\right)\)

Bác Mặt trời thức dậy sau lũy tre làng 

\(...\Leftrightarrow x\left(y+1\right)+y+1=0\Leftrightarrow\left(x+1\right)\left(y+1\right)=0\)  \(\Leftrightarrow\left[{}\begin{matrix}x=-1\\y=-1\end{matrix}\right.\)

... \(\Leftrightarrow\sqrt{\left(x-2\right)^2}=\sqrt{\left(\sqrt{2}+1\right)^2}\)   \(\Leftrightarrow\left|x-2\right|=\sqrt{2}+1\)  \(\Leftrightarrow\left[{}\begin{matrix}x-2=\sqrt{2}+1\\x-2=-\sqrt{2}-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}+3\\x=-\sqrt{2}+1\end{matrix}\right.\)

\(\Delta ABC\) có : x + y + \(\widehat{ACB}\) = 180^o  ( tổng 3 góc trong 1 \(\Delta\) )

Mà \(\widehat{ACB}+z=180^o\) \(\Rightarrow z=x+y\left(đpcm\right)\)

a) B/t x/đ \(\Leftrightarrow2x+10\ge0\Leftrightarrow x\ge-5\)

b) B/t x/đ \(\Leftrightarrow4x^2-36\ge0\Leftrightarrow x^2\ge9\)  \(\Leftrightarrow\left[{}\begin{matrix}x\le-3\\x\ge3\end{matrix}\right.\)

a) \(A=...=sin\left(90^o-49^o\right)+tan40^o.tan\left(90^o-40^o\right)-cos49^o\)

\(=cos49^o+tan40^o.cot40^o-cos49^o=1\)

b) \(B=...=\left(sin^241+sin^249^o\right)+\left(sin^243^o+sin^247^o\right)+\left(sin^244^o+sin^246^o\right)\)

\(=\left(sin^249^o+cos^249^o\right)+\left(sin^243^o+cos^243^o\right)+\left(sin^244^o+cos^244^o\right)=1+1+1=3\)