A = 2x² + 6x = 2( x² + 3x + 9/4 ) - 9/2 = 2( x + 3/2 )² - 9/2 ≥ -9/2 ∀ x

Dấu "=" xảy ra khi x = -3/2

=> MinA = -9/2 <=> x = -3/2

B = x² - 2x + y² - 4y + 6 = ( x² - 2x + 1 ) + ( y² - 4y + 4 ) + 1 = ( x - 1 )² + ( y - 2 )² + 1 ≥ 1 ∀ x, y

Dấu "=" xảy ra khi x = 1 ; y = 2

=> MinB = 1 <=> x = 1 ; y = 2

C = x² - 2xy + 6y² - 12x + 2y + 45

= ( x² - 2xy + y² - 12x + 12y + 36 ) + ( 5y² - 10y + 5 ) + 4

= [ ( x² - 2xy + y² ) - ( 12x - 12y ) + 36 ] + 5( y² - 2y + 1 ) + 4

= [ ( x - y )² - 2( x - y ).6 + 6² ] + 5( y - 1 )² + 4

= ( x - y - 6 )² + 5( y - 1 )² + 4 ≥ 4 ∀ x, y

Dấu "=" xảy ra khi x = 7 ; y = 1

=> MinC = 4 <=> x = 7 ; y = 1

D = ( x - 1 )( x + 2 )( x + 3 )( x + 6 )

= [ ( x - 1 )( x + 6 ) ][ ( x + 2 )( x + 3 ) ]

= ( x² + 5x - 6 )( x² + 5x + 6 )

= ( x² + 5x )² - 36 ≥ -36 ∀ x

Dấu "=" xảy ra <=> x² + 5x = 0

                        <=> x( x + 5 ) = 0

                        <=> x = 0 hoặc x = -5

=> MinD = -36 <=> x = 0 hoặc x = -5

a) \(x\left(x-2\right)-7x+14=0\)

\(\Leftrightarrow x\left(x-2\right)-7\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-7\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=7\end{cases}}\)

b) \(x^2\left(x-3\right)+12-4x=0\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x=3\\x^2=4\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=\pm2\end{cases}}\)

c) \(x^2+12x-13=0\)

\(\Leftrightarrow\left(x^2-x\right)+\left(13x-13\right)=0\)

\(\Leftrightarrow x\left(x-1\right)+13\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+13\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-13\end{cases}}\)

d) \(4x^2-4x=8\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)

e) \(x^2-6x=1\)

\(\Leftrightarrow\left(x-3\right)^2=10\)

\(\Leftrightarrow\orbr{\begin{cases}x-3=\sqrt{10}\\x-3=-\sqrt{10}\end{cases}}\Rightarrow\orbr{\begin{cases}x=3+\sqrt{10}\\x=3-\sqrt{10}\end{cases}}\)

a) x( x - 2 ) - 7x + 14 = 0

<=> x( x - 2 ) - 7( x - 2 ) = 0

<=> ( x - 2 )( x - 7 ) = 0

<=> \(\orbr{\begin{cases}x-2=0\\x-7=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=7\end{cases}}\)

b) x²( x - 3 ) + 12 - 4x = 0

<=> x²( x - 3 ) - 4( x - 3 ) = 0

<=> ( x - 3 )( x² - 4 ) = 0

<=> \(\orbr{\begin{cases}x-3=0\\x^2-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=\pm2\end{cases}}\)

c) x² + 12x - 13 = 0

<=> x² - x + 13x - 13 = 0

<=> x( x - 1 ) + 13( x - 1 ) = 0

<=> ( x - 1 )( x + 13 ) = 0

<=> \(\orbr{\begin{cases}x-1=0\\x+13=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x=-13\end{cases}}\)

d) 4x² - 4x = 8

<=> 4( x² - x ) = 8

<=> x² - x = 2

<=> x² - x - 2 = 0

<=> x² + x - 2x - 2 = 0

<=> x( x + 1 ) - 2( x + 1 ) = 0

<=> ( x + 1 )( x - 2 ) = 0

<=> \(\orbr{\begin{cases}x+1=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)

e) x² - 6x = 1

<=> x² - 6x + 9 = 1 + 9

<=> ( x - 3 )² = 10

<=> ( x - 3 )² = ( ±√10 )²

<=> \(\orbr{\begin{cases}x-3=\sqrt{10}\\x-3=-\sqrt{10}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=3+\sqrt{10}\\x=3-\sqrt{10}\end{cases}}\)

a) \(4x^3y-12x^2y^3-8x^4y^3\)

\(=4x^2y\left(x-3y^2-2x^2y^2\right)\)

b) \(2x^2+4x+2-2y^2\)

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

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

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

c) \(x^3-2x^2+x-xy^2\)

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

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

\(=x\left(x-y-1\right)\left(x+y-1\right)\)

d) \(x\left(x-2y\right)+3\left(2y-x\right)\)

\(=x\left(x-2y\right)-3\left(x-2y\right)\)

\(=\left(x-3\right)\left(x-2y\right)\)

e) \(x^2+4\)

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

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

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

f) \(5x^2-7x-6\)

\(=\left(5x^2-10x\right)+\left(3x-6\right)\)

\(=5x\left(x-2\right)+3\left(x-2\right)\)

\(=\left(5x+3\right)\left(x-2\right)\)

3425627829^{44525266272177437674677263632625654354}=\(\infty\)

(x - 1)³ - (x + 1)³ + 6(x + 1)(x - 1)

= x³ - 3x² + 3x - 1 - (x³ + 3x² + 3x + 1) + 6(x²  - 1)

= x³ - 3x² + 3x - 1 - x³ - 3x² - 3x  - 1 +6x² - 6

= (x³ - x³) + (-3x² - 3x² + 6x²) + (3x - 3x) + (-1 - 1 - 6) = -8

    \(\left(x-1\right)^3-\left(x+1\right)^3+6.\left(x+1\right).\left(x-1\right)\)

\(=x^3-3x^2+3x-1-\left(x^3+3x^2+3x+1\right)+6.\left(x^2-1\right)\)

\(=x^3-3x^2+3x-1-x^3-3x^2-3x-1+6x^2-6\)

\(=-8\)