x² + 2x + 2 = 0

<=> (x² + 2x + 1) + 1 = 0

<=> (x + 1)² = -1

Làm gì có x mà tính :))

https://hoc24.vn/hoi-dap/question/718676.html?pos=1958928

Lời giải:
Ta có:

\(M=x^4+16x+2007=x^2(x^2+2x-2)-2x^3+2x^2+16x+2007\)

\(=x^2(x^2+2x-2)-2x(x^2+2x-2)+6x^2+12x+2007\)

\(=x^2(x^2+2x-2)-2x(x^2+2x-2)+6(x^2+2x-2)+2019\)

\(=(x^2-2x+6)(x^2+2x-2)+2019=(x^2-2x+6).0+2019=2019\)

x²-x = 0 <=> x (x-1) = 0 <=> x = 0 hoặc x= 1

Với x = 0 ta có : B = 2.0⁴-11.0³+11.0²-16.0+5 = 5

Với x = 1 ta có : B = 2.1⁴-11.1³+11.1²-16.1+5 = -9

Đêm Noel..Đêm Noel~~~...Ma gõ cửa nhà em:))...Em đi ra~~~~Phi xe ga......Đâm chết năm con gà=)))))))...hố hố...... ~Merry Christmas~ ^-^ Noel đến đít rùi:))

Đẳng thức: \(5x^2+5y^2+8xy-2x+2y+2=0\)

\(\Leftrightarrow\left(4x^2+8xy+4y^2\right)+\left(x^2-2x+1\right)+\left(y^2+2y+1\right)=0\)

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

\(\Leftrightarrow4\left(x+y\right)^2+\left(x-1\right)^2+\left(y+1\right)^2=0\)

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

Thay vào \(M=\left(x+y\right)^{2007}+\left(x-2\right)^{2008}+\left(y+1\right)^{2009}\) ta được:

\(M=\left(1-1\right)^{2007}+\left(1-2\right)^{2008}+\left(-1+1\right)^{2009}=\left(-1\right)^{2008}=1\)

Ta có:

\(5x^2+5y^2+8xy-2x+2y+2=0\)

\(\Leftrightarrow x^2+4x^2+y^2+4y^2+8xy-2x+2y+1+1=0\)

\(\Leftrightarrow\left(x^2-2x+1\right)+\left(y^2+2y+1\right)+\left(4x^2+8xy+4y^2\right)=0\)

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

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

Mà: \(\left\{{}\begin{matrix}\left(x-1\right)^2\ge0\\\left(y+1\right)^2\ge0\\4\left(x+y\right)^2\ge0\end{matrix}\right.\Leftrightarrow\left(x-1\right)^2+\left(y+1\right)^2+4\left(x+y\right)^2\ge0\)

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

Thay giá trị x và y vào M ta có:

\(M=\left(x+y\right)^{2007}+\left(x-2\right)^{2008}+\left(y+1\right)^{2009}\)

\(M=\left(1-1\right)^{2007}+\left(1-2\right)^{2008}+\left(-1+1\right)^{2009}\)

\(M=0^{2007}+\left(-1\right)^{2008}+0^{2009}\)
\(M=\left(-1\right)^{2008}\)

\(M=1\)

\(x^3-x^2-x-2=0\)

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

\(x^2+x+1=x^2+2\cdot\frac{1}{2}\cdot x+\frac{1}{4}+\frac{3}{4}=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)

\(x^2+x+1\ne0\Rightarrow x-2=0\Rightarrow x=2\)

\(x^9-8x^3+16x^2-2x+2012\)

\(2^9-8\cdot2^3+16\cdot2^2-2\cdot2+2012=2520\)

Vậy...

Ta có: \(x^3-x^2-x-2=0\)

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

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

Vì \(x^2+x+1=x^2+2.\frac{1}{2}.x+\frac{1}{4}+\frac{3}{4}=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)

nên \(x^2+x+1\ne0\)

\(\Rightarrow x-2=0\Rightarrow x=2\)

Tiếp tục thay vào biểu thức cần tìm ,ta được:

\(x^9-8x^3+16x^2-2x+2012\)

\(2^9-8.2^3+16.2^2-2.2+2012=2520\)