A = 10x² + y² + 4z² + 6x - 4y - 4xz + 2024

= ( x² - 4xz + 4z² ) + ( 9x² + 6x + 1 ) + ( y² - 4y + 4 ) + 2019

= ( x - 2z )² + ( 3x + 1 )² + ( y - 2 )² + 2019 ≥ 2019 ∀ x, y, z

Dấu "=" xảy ra <=> \(\hept{\begin{cases}x-2z=0\\3x+1=0\\y-2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-\frac{1}{3}\\y=2\\z=-\frac{1}{6}\end{cases}}\)

=> MinA = 2019 <=> \(\hept{\begin{cases}x=-\frac{1}{3}\\y=2\\z=-\frac{1}{6}\end{cases}}\)

cái này = 0 à bạn????

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

\(\Leftrightarrow\left(2x-3\right).\left(3x+2-2x+3\right)=0\)( chỗ này đổi dấu nhá)

\(\Leftrightarrow\left(2x-3\right).\left(x+5\right)=0\Leftrightarrow\orbr{\begin{cases}2x-3=0\\x+5=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=-5\end{cases}}\)

Cậu tham khảo ạ, chúc cậu học tốt '.'

a) ax + ay - bx - by = ( ax - bx ) + ( ay - by ) = x( a - b ) + y( a - b ) = ( a - b )( x + y ) < đã sửa >

b) 2x² - 6xy + 5x - 15y = 2x( x - 3y ) + 5( x - 3y ) = ( x - 3y )( 2x + 5 )

c) ( a + b )² - 4a² = ( a + b )² - ( 2a )² = ( a + b - 2a )( a + b + 2a ) = ( b - a )( b + 3a )

d) 5a²xy - 10a³x - 15a²x² = 5a²x( y - 2a - 3x )

e) 3( x - 1 ) + 5x( x - 1 ) = ( x - 1 )( 3 + 5x )

f) 9a² - 4 = ( 3a )² - 2² = ( 3a - 2 )( 3a + 2 )

g) 2x³ + 8x⁴ + 8x = 2x( x + 4x² + 4 ) 

h) a² - 4 + 4b - b² = a² - ( b² - 4b + 4 ) = a² - ( b - 2 )² = ( a - b + 2 )( a + b - 2 )

i) a² + 2ab + b² - 16 = ( a² + 2ab + b² ) - 16 = ( a + b )² - 4² = ( a + b - 4 )( a + b + 4 )

k) x² + 5x + 4 = x² + x + 4x + 4 = x( x + 1 ) + 4( x + 1 ) = ( x + 1 )( x + 4 )

l) 2x² - 3x - 5 = 2x² + 2x - 5x - 5 = 2x( x + 1 ) - 5( x + 1 ) = ( x + 1 )( 2x - 5 )

m) x³ + 6x² + 9x = x( x² + 6x + 9 ) = x( x + 3 )²

A = -x² + x - 3 = -( x² - x + 1/4 ) - 11/4 = -( x - 1/2 )² - 11/4 ≤ -11/4 < 0 ∀ x ( đpcm )

B = -4x² + 4x - 5 = -( 4x² - 4x + 1 ) - 4 = -( 2x - 1 )² - 4 ≤ -4 < 0 ∀ x ( đpcm )

C = -x² + 4x - 6 = -( x² - 4x + 4 ) - 2 = -( x - 2 )² - 2 ≤ -2 < 0 ∀ x ( đpcm )

A = x² + 6x + 11 = ( x² + 6x + 9 ) + 2 = ( x + 3 )² + 2 ≥ 2 > 0 ∀ x ( đã sửa )

B = x² - 4x + 12 = ( x² - 4x + 4 ) + 8 = ( x - 2 )² + 8 ≥ 8 > 0 ∀ x ( đpcm )

C = x² + 4x + 6 = ( x² + 4x + 4 ) + 2 = ( x + 2 )² + 2 ≥ 2 > 0 ∀ x ( đpcm )

D = x² - 2x + 5 = ( x² - 2x + 1 ) + 4 = ( x - 1 )² + 4 ≥ 4 > 0 ∀ x ( đpcm )

a) \(x^2-xy+4x-2y+4\)

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

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

b) \(2x^2-5x-3\)

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

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

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

c)\(\)

c);d);e) tạm thời tớ chưa nghĩ ra-.-"

tham khả tạm 2 câu ạ, chúc học tốt'.'