19.9-63x+18=0

-63x= -(171+18)

-63x= -189

x=189:63

x=3

\(x^4-4x^3-5x^2-3x^2+12x+15=0\)

\(\Leftrightarrow x^2\left(x^2-4x-5\right)-3\left(x^2-4x-5\right)=0\)

\(\Leftrightarrow\left(x^2-3\right)\left(x^2-4x-5\right)=0\)

\(x^4-4x^3-8x^2+12x+15=0\)

\(\Leftrightarrow x^4+x^3-5x^3-5x^2-3x^2-3x+15x+15=0\)

\(\Leftrightarrow x^3\left(x+1\right)-5x^2\left(x+1\right)-3x\left(x+1\right)+15\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^3-5x^2-3x+15\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left[x^2\left(x-5\right)-3\left(x-5\right)\right]=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-5\right)\left(x^2-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-5=0\\x^2=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=5\\x=\pm\sqrt{3}\end{matrix}\right.\)

Phân tích thành nhân tử ta được:

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

Vậy \(\left[{}\begin{matrix}x=-1\\x=5\\x=\pm\sqrt{3}\end{matrix}\right.\)

1) \(A=\left(2x^2+1\right)^4-3\ge0-3=-3\) (do \(\left(2x^2+1\right)^4\ge0\forall x\))

Dấu "=" xảy ra \(\Leftrightarrow\left(2x^2+1\right)=0\Leftrightarrow2x^2=-1\Leftrightarrow x^2=-\frac{1}{2}\) (vô lí)

Vậy đề sai ~v  (hay là tui làm sai ta)

1b) \(B=3\left|1-2x\right|-5\ge0-5=-5\)  (do \(\left|1-2x\right|\ge0\forall x\))

Dấu "=" xảy ra khi \(\left|1-2x\right|=0\Leftrightarrow2x=1\Leftrightarrow x=\frac{1}{2}\)

Vậy \(B_{min}=-5\Leftrightarrow x=\frac{1}{2}\)

@tth T làm cũng ra như vậy @@

1) \(x^4-6x^3-x^2+54x-72=0\)

\(\Leftrightarrow x^3\left(x-2\right)-4x^2\left(x-2\right)-9x\left(x-2\right)+36\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-4x^2-9x+36\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x-4\right)-9\left(x-4\right)\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-4\right)\left(x^2-9\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-4\right)\left(x-3\right)\left(x+3\right)=0\)

Tự làm nốt...

2) \(x^4-5x^2+4=0\)

\(\Leftrightarrow x^2\left(x^2-1\right)-4\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)

Tự làm nốt...

\(x^4-2x^3-6x^2+8x+8=0\)

\(\Leftrightarrow x^3\left(x-2\right)-6x\left(x-2\right)-4\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-6x-4\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x+2\right)-2x\left(x+2\right)-2\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x^2-2x-2\right)=0\)

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

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-1-\sqrt{3}\right)\left(x-1+\sqrt{3}\right)=0\)

...

\(2x^4-13x^3+20x^2-3x-2=0\)

\(\Leftrightarrow2x^3\left(x-2\right)-9x^2\left(x-2\right)+2x\left(x-2\right)+\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(2x^3-9x^2+2x+1\right)=0\)

Bí

\(2x^3-9x^2+2x+1\)

\(=2x^3-x^2-8x^2+4x-2x+1\)

\(=x^2\left(2x-1\right)-4x\left(2x-1\right)-\left(2x-1\right)\)

\(=\left(2x-1\right)\left(x^2-4x-1\right)\)

\(=\left(2x-1\right)\left(x^2-4x+4-5\right)\)

\(=\left(2x-1\right)\left[\left(x-2\right)^2-5\right]\)

.......

\(\Leftrightarrow\sqrt{x+4}\left(\sqrt{x-4}-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-4=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=8\end{matrix}\right.\)

158:x=20.7

158:x=140

x=158:140

x=1,1285......

x=79/70

-3^4 x 4^4 = (-3 x 4)^4 = (-12)^4

2^2 x 6^2 = (2 x 6)^2 = 12^2

(-12)^4 / 12^2 = 144