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\(A=9y^2+12x^2-6xy+12y-6x+200\)
Rút gọn A ta có:
\(A=y\left(9y-12\right)+x\left(12x-6-6y\right)+200\)
\(MinA=0\Leftrightarrow y\left(9y-12\right)+x\left(12x-6-6y\right)=-200\)
Trả lời:
7, 5( x + y )2 + 15( x + y )
= 5( x + y )( x + y + 3 )
9, 7x( y - 4 )2 - ( 4 - y )3
= 7x ( 4 - y )2 - ( 4 - y )
= ( 4 - y )2 ( 7x - 4 + y )
11, ( x + 1 )( y - 2 ) - ( 2 - y )2
= ( x + 1 )( y - 2 ) - ( y - 2 )2
= ( y - 2 )( x + 1 - y + 2 )
= ( y - 2 )( x - y + 3 )
8, 9x ( x - y ) - 10 ( y - x )2
= 9x ( x - y ) - 10 ( x - y )2
= ( x - y )[ ( 9x - 10 ( x - y ) ]
= ( x - y )( 9x - 10x + 10y )
= ( x - y )( 10y - x )
10, ( a - b )2 - ( a + b )( b - a )
= ( b - a )2 - ( a + b )( b - a )
= ( b - a )( b - a - a - b )
= - 2a( b - a )
= 2a ( a - b )
12, 2x ( x - 3 ) + y ( x - 3 ) + ( 3 - x )
= 2x ( x - 3 ) + y ( x - 3 ) - ( x - 3 )
= ( x - 3 )( 2x + y - 1 )
a. \(-4x^2-4x-2\)
\(=-\left(4x^2+4x+2\right)\)
\(=-\left[\left(2x\right)^2+2.2x+1+1\right]\)
\(=-\left[\left(2x+1\right)^2+1\right]\)
\(=-\left(2x+1\right)^2-1\)
vì \(\left(2x+1\right)^2\ge0\forall x\Rightarrow-\left(2x+1\right)^2\le0\forall x\)
\(\Rightarrow-\left(2x+1\right)^2-1\le-1\forall x\)hay \(-4x^2-4x-2< 0\)
b. \(x^2+x+1\)
\(=x^2+2.\frac{1}{2}x+\left(\frac{1}{2}\right)^2+\frac{3}{4}\)
\(=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)
chúc bạn học tốt, k đúng cho mình nha, cảm ơn b
a)
\(x^2+6x+9\)
\(\Leftrightarrow\left(x+3\right)^2\)
b) \(\frac{1}{4}x^2-\frac{1}{2}x+1\)
\(\Leftrightarrow\left(\frac{1}{2}-x\right)^2\)
#Cừu
\(\left(ab+cd\right)^2=\left(ab\right)^2+\left(cd\right)^2=a^2b^2c^2d^2=ab.ab+cd.cd\ge k\)abcd
\(\Leftrightarrow Max\)\(k=15\)
phân tích đa thức thành nhân tử hả bạn ?
a, \(x^2+2xy+x+2y=x\left(x+2y\right)+x+2y=\left(x+1\right)\left(x+2y\right)\)
b, \(x^2-4x+4-y^2=\left(x-2\right)^2-y^2=\left(x-2-y\right)\left(x-2+y\right)\)
a) = ( x - 3 )2 - ( 3x )2 = ( -2x - 3 )( 4x - 3 )
b) = x( x - 2y ) - ( x - 2y ) = ( x - 2y )( x - 1 )
a) \(\left(x-3-3x\right).\left(x-3+3x\right)\)
b) \(\left(x-2y\right).\left(x-1\right)\)
Trả lời:
1, 5 ( x + y )2 + 15 ( x + y )
= 5( x + y ) ( x + y + 3 )
2, ( a - b )2 - ( a + b )( b - a )
= ( a - b )2 + ( a + b )( a - b )
= ( a - b )( a - b + a + b )
= 2a ( a - b )