Bài 2 : 

a, \(x^2-4x=0\Leftrightarrow x\left(x-4\right)=0\Leftrightarrow x=0;4\)

b, \(5x\left(x-2020\right)-x+2020=0\)

\(\Leftrightarrow5x\left(x-2020\right)-\left(x-2020\right)=0\Leftrightarrow\left(5x-1\right)\left(x-2020\right)=0\)

\(\Leftrightarrow x=\frac{1}{5};2020\)

c, \(\left(4x+5\right)^2-\left(2x-1\right)^2=0\)

\(\Leftrightarrow16x^2+40x+25-\left(4x^2-4x+1\right)=0\)

\(\Leftrightarrow12x^2+44x+24=0\Leftrightarrow4\left(x+3\right)\left(3x+2\right)=0\)

\(\Leftrightarrow x=-3;-\frac{2}{3}\)

a,x²-4x=0

= x.(x-4)=0

=> x=0 hoặc x-4=0

=>x=0 hoặc x=4

a. x² - 4x = 0

<=> x ( x - 4 ) = 0

<=>\(\orbr{\begin{cases}x=0\\x=-4\end{cases}}\)

b. 5x ( x - 2020 ) - x + 2020 = 0

<=> 5x ( x - 2020 ) - ( x - 2020 ) = 0

<=> ( 5x - 1 ) ( x - 2020 ) = 0

<=>\(\orbr{\begin{cases}5x-1=0\\x-2020=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=\frac{1}{5}\\x=2020\end{cases}}\)

c. ( 4x + 5 )² - ( 2x - 1 )² = 0

<=> 16x² + 40x + 25 - 4x² + 4x - 1 = 0

<=> 12x² + 44x + 24 = 0

<=> 4 ( 3x² + 11x + 6 ) = 0

<=> ( 3x² + 9x ) + ( 2x + 6 ) = 0

<=> 3x ( x + 3 ) + 2 ( x + 3 ) = 0

<=> ( 3x + 2 ) ( x + 3 ) = 0

<=>\(\orbr{\begin{cases}3x+2=0\\x+3=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=-\frac{2}{3}\\x=-3\end{cases}}\)

d. x² + 6x - 8 = 0

<=> x² + 6x + 9 = 17

<=> ( x + 3 )² = 17 

<=>\(\orbr{\begin{cases}x+3=\sqrt{17}\\x+3=-\sqrt{17}\end{cases}}\)<=>\(\orbr{\begin{cases}x=-3+\sqrt{17}\\x=-3-\sqrt{17}\end{cases}}\)

e. 4x² + 2x - 6 = 0

<=> 2 ( 2x² + x - 3 ) = 0

<=> ( 2x² + 3x ) - ( 2x + 3 ) = 0

<=> x ( 2x + 3 ) - ( 2x + 3 ) = 0

<=> ( x - 1 ) ( 2x + 3 ) = 0

<=>\(\orbr{\begin{cases}x-1=0\\2x+3=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=1\\x=-\frac{3}{2}\end{cases}}\)

\(A=x^2-20x+101\)

\(A=x^2-2\cdot x\cdot10+100+1\)

\(A=\left(x-10\right)^2+1\ge1\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow x=10\)

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\(B=4a^2+4a+2\)

\(B=4a^2+4a+1+1\)

\(B=\left(2a+1\right)^2+1\ge1\forall a\)

Dấu "=" xảy ra \(\Leftrightarrow a=\frac{-1}{2}\)

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\(C=x^2-4xy+5y^2+10x-22y+28\)

\(C=x^2-4xy+4y^2+y^2+10x-22y+28\)

\(C=\left(x-2y\right)^2+2\cdot\left(x-2y\right)\cdot5+25+y^2-2y+1+2\)

\(C=\left(x-2y+5\right)^2+\left(y-1\right)^2+2\ge2\forall x;y\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x-2y+5=0\\y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=1\end{matrix}\right.\)

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\(D=4x-x^2+3\)

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

\(D=-\left(x^2-4x+4-7\right)\)

\(D=-\left[\left(x-2\right)^2-7\right]\)

\(D=7-\left(x-2\right)^2\le7\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow x=2\)

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\(E=x-x^2\)

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

\(E=-\left(x^2-2\cdot x\cdot\frac{1}{2}+\frac{1}{4}-\frac{1}{4}\right)\)

\(E=-\left[\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\right]\)

\(E=\frac{1}{4}-\left(x-\frac{1}{2}\right)^2\le\frac{1}{4}\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow x=\frac{1}{2}\)

a, \(A=x^2-20x+101=x^2-2.x.10+10^2+1\)

\(=\left(x-10\right)^2+1\ge1\)

Dấu "=" xảy ra \(\Leftrightarrow\left(x-10\right)^2=0\)

\(\Leftrightarrow x-10=0\)

\(\Leftrightarrow x=10\)

Vậy : \(A_{min}=1\Leftrightarrow x=10\)

b) \(B=4a^2+4a+2=\left(2a\right)^2+2.2a.1+1^2+1\)

\(=\left(2a+1\right)^2+1\ge1\)

Dấu "=" xảy ra \(\Leftrightarrow\left(2a+1\right)^2=0\)

\(\Leftrightarrow2a+1=0\)

\(\Leftrightarrow2a=-1\)

\(\Leftrightarrow a=-\frac{1}{2}\)

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

a) Có x = 99 => x+1 = 100

A = x⁵ - (x+1)x⁴ + (x+1)x³ + (x+1)x² + (x+1)x - 9

= x⁵ - x⁵ + x⁴ - x⁴ + x³ - x³ + x² - x² + x - 9

= x - 9

=> A = 90

b) Chữa đề: x⁶ - 20x⁵ - 20x⁴ - 20x³ - 20x² - 20x + 3

Có: x = 21 => x-1 = 20

B = x⁶ - (x-1)x⁵ - (x-1)x⁴ - (x-1)x³ - (x-1)x² - (x-1)x + 3

= x⁶ - x⁶ + x⁵ - x⁵ + x⁴ - x⁴ + x³ - x³ + x² - x + 3

= x + 3

=> B = 24

Ta có: \(5^{4x}:5^5=5^{2020}:5^{2019}\)

    \(\Leftrightarrow5^{4x-5}=5^1\)

    \(\Leftrightarrow4x-5=1\)

    \(\Leftrightarrow4x=6\)

    \(\Leftrightarrow x=\frac{3}{2}\left(L\right)\)

Vậy \(x=\varnothing\)

\(A=x^2-6x+10=\left(x-3\right)^2+1\ge1\)

\(\Rightarrow A_{min}=1\Leftrightarrow x=3\)

\(B=4x^2-4x+25=\left(2x-1\right)^2+24\ge24\)

\(\Rightarrow B_{min}=24\Leftrightarrow x=\frac{1}{2}\)

\(C=3x^2+9x+12=3\left(x+\frac{3}{2}\right)^2+\frac{21}{4}\ge\frac{21}{4}\)

\(\Rightarrow C_{min}=\frac{21}{4}\Leftrightarrow x=\frac{-3}{2}\)

b \(\Leftrightarrow x^3\left(x-2\right)+10x\left(x-2\right)=0\)

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

hay \(x\in\left\{0;2\right\}\)

c: \(\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)

=>(x-8)(3x+2)=0

=>x=8 hoặc x=-2/3

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

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

=>x=2 hoặc x=1

e: \(\Leftrightarrow x\left(x^2-11x+30\right)=0\)

=>x(x-5)(x-6)=0

hay \(x\in\left\{0;5;6\right\}\)

b: \(\Leftrightarrow x\left(x^3-2x^2+10x-20\right)=0\)

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

hay \(x\in\left\{0;2\right\}\)

c: \(\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)

=>(x-8)(3x+2)=0

hay \(x\in\left\{8;-\dfrac{2}{3}\right\}\)

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

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

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

=>x=1 hoặc x=2

bn kiểm tra giúp mk đề 2 câu cuối , mk làm ko ra

Khó quá,hay quá !!!

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

2. \(x^2+5x+\dfrac{25}{4}=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)

3. \(16x^2-8x+1=\left(4x-1\right)^2\)

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

5. \(\dfrac{1}{4}x^2-\dfrac{4}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)\left(\dfrac{1}{2}x+\dfrac{2}{3}y\right)\)

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

7. \(4x^2-20x+25-y^2=\left(2x-5\right)^2-y^2=\left(2x-5-y\right)\left(2x-5+y\right)\)

Kết quả nè

1.(x^2-1)^2×(x^2+1)^2

2.(2x-5)^2÷4

3.(4x-1)^2

4.(x+y)^2×(x-y)

5.(1/4x-4/9y)×(1/4x+1/9y)