2xⁿ⁺¹ (x^n-1 - y^n-1) - y^n-1 (2xⁿ⁺¹ - yⁿ⁺¹)

= 2x²ⁿ -2xⁿ⁺¹ y^n-1 - y^n-1 2xⁿ⁺¹ +y²ⁿ

= 2x²ⁿ + y²ⁿ - 4xⁿ⁺¹ y^n-1

2x²-x+1/3-2/3x=0

6x²-5x+1=0

6x²-3x-2x+1=0

(x-1)(2x-1)=0

x-1=0 và 2x=1

x=1 và x=1/2

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

\(\Leftrightarrow2x^2-x+\frac{1}{3}-\frac{2x}{3}=0\)

\(\Leftrightarrow2x^2-\frac{5}{3}x+\frac{1}{3}=0\)

\(\Leftrightarrow\frac{6x^2-5x+1}{3}=0\)

\(\Leftrightarrow6x^2-5x+1=0\)

\(\Leftrightarrow6x^2-2x-3x+1=0\)

\(\Leftrightarrow2x\left(3x-1\right)-\left(3x-1\right)=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}3x-1=0\\2x-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x=1\\2x=1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=\frac{1}{2}\end{cases}}\)

Vậy \(S=\left\{\frac{1}{3};\frac{1}{2}\right\}\)

x² - 4x + 2 = ( x² - 4x + 4 ) - 2 = ( x - 2 )² - 2 ≥ -2 ∀ x

Dấu "=" xảy ra <=> x = 2 . Vậy GTNN của bthuc = -2

x^2 - 4x + 2 

= x^2 - 4x + 4 - 2 

= ( x - 2 ) ^2 - 2 

 \(\left(x-2\right)^2\ge0\forall x\)

\(\left(x-2\right)^2-2\ge-2\)   

Dấu = xảy ra khi và chỉ khi 

 x - 2 = 0 

x = 0 + 2 

x = 2 

vậy min = -2 khi và chỉ khi x = 2 

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

\(=x\left(y-z\right)\left(y+z\right)+yz^2-yx^2+zx^2-zy^2\)

\(=\left(y-z\right)\left[x.\left(y+z\right)\right]-x^2\left(y-z\right)-yz\left(y-z\right)\)

\(=\left(y-z\right)\left(xy+xz\right)-x^2\left(y-z\right)-yz\left(y-z\right)\)

\(=\left(y-z\right)\left(xy+xz-x^2-yz\right)\)

\(=\left(y-z\right)\left[\left(xy-x^2\right)+\left(xz-yz\right)\right]\)

\(=\left(y-z\right)\left[x\left(y-x\right)-z\left(y-x\right)\right]\)

\(=\left(y-z\right)\left(y-x\right)\left(x-z\right)\)

x² - 4xy + 4y² - x + 2y

= ( x - 2y )² - ( x - 2y )

= ( x - 2y )( x - 2y - 1 )

x^2 - 4x + 4 = 5 ( x - 2 ) 

x^2 - 4x + 4 - 5 ( x - 2 ) = 0 

( x - 2 ) ^2 - 5 ( x - 2 ) = 0 

( x - 2 ) ( x - 2 - 5 ) = 0

( x - 2 ) ( x - 7 ) = 0 

x  - 2 = 0 hoặc x - 7 = 0 

x = 2 hoặc x = 7 

c) (x-2)^2=5(x-2)

=> x-2=5 hoặc x-2 =0

=> x=7 hoặc x=2

d) (2x-3)^2=(5-x)^2

=> 2x-3=5-x

=> x=8/3

a+b=7 suy ra (a+b)²=49 suy ra a²+2ab+b²=49 suy ra a²+2.3+b²=49 suy ra a²+b²=43

Ta có :

 \(a^2+b^2\)

\(=a^2+2ab+b^2-2ab\)

\(=\left(a+b\right)^2-2ab\)

\(=7^2-2.3\)

\(=43\)

       Ps: k cho tớ nhé

                                                                                                                                                      # Aeri # 

144a² - 81 = 9( 16a² - 9 ) = 9( 4a - 3 )( 4a + 3 )

36a² - 49b² = ( 6a - 7b )( 6a + 7b )

a² - 4b² = ( a - 2b )( a + 2b )

1/4a² - b² = ( 1/2a - b )( 1/2a + b )

4/9a⁴ - 25/4 = ( 2/3a² - 5/2 )( 2/3a² + 5/2 )