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Ta có : x2 - 4x + y2 + 2y + 5 = 0
<=> (x2 - 4x + 4) + (y2 + 2y + 1) = 0
<=> (x - 2)2 + (y + 1)2 = 0
Mà (x - 2)2 \(\ge0\forall x\)
(y + 1)2 \(\ge0\forall x\)
Nên \(\orbr{\begin{cases}\left(x-2\right)^2=0\\\left(y+1\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\y+1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\y=-0\end{cases}}\)
1a : x = -1
2a : x = 10
còn mấy bài khác mình không biết giải nha
Bài 1:
a ) \(Q=\dfrac{3}{2}x^2+x+1=\dfrac{3}{2}\left(x^2+\dfrac{2}{3}x+\dfrac{2}{3}\right)=\dfrac{3}{2}\left(x^2+\dfrac{2}{3}x+\dfrac{1}{9}+\dfrac{5}{9}\right)=\dfrac{3}{2}\left[\left(x+\dfrac{1}{3}\right)^2+\dfrac{5}{9}\right]=\dfrac{3}{2}\left(x+\dfrac{1}{3}\right)^2+\dfrac{5}{6}\ge\dfrac{5}{6}\forall x\)
Dấu " = " xảy ra \(\Leftrightarrow x+\dfrac{1}{3}=0\Leftrightarrow x=-\dfrac{1}{3}\)
Vậy Min Q là : \(\dfrac{5}{6}\Leftrightarrow x=-\dfrac{1}{3}\)
b ) \(R=x^2+2y^2+2xy-2y=\left(x^2+2xy+y^2\right)+\left(y^2-2y+1\right)-1=\left(x+y\right)^2+\left(y-1\right)^2-1\ge-1\forall x;y\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-y\\y=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=1\end{matrix}\right.\)
Vậy Min R là : \(-1\Leftrightarrow x=-1;y=1\)
Bài 2 :
a ) \(Q=2x-2-3x^2\)
\(=-3\left(x^2-\dfrac{2}{3}x+\dfrac{2}{3}\right)\)
\(=-3\left(x^2-\dfrac{2}{3}x+\dfrac{1}{9}+\dfrac{5}{9}\right)\)
\(=-3\left[\left(x-\dfrac{1}{3}\right)^2+\dfrac{5}{9}\right]\)
\(=-3\left(x-\dfrac{1}{3}\right)^2-\dfrac{5}{3}\le-\dfrac{5}{3}\forall x\)
Dấu " = " xảy ra \(\Leftrightarrow x-\dfrac{1}{3}=0\Leftrightarrow x=\dfrac{1}{3}\)
Vậy Max Q là : \(-\dfrac{5}{3}\Leftrightarrow x=\dfrac{1}{3}\)
b ) \(2-x^2-y^2-2\left(x+y\right)\)
\(=2-x^2-y^2-2x-2y\)
\(=-\left(x^2+2x+1\right)-\left(y^2+2y+1\right)+4\)
\(=-\left(x+1\right)^2-\left(y+1\right)^2+4\le4\forall x;y\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+1=0\\y+1=0\end{matrix}\right.\) \(\Leftrightarrow x=y=-1\)
Vậy Max của b/t trên là : \(4\Leftrightarrow x=-1\)
c ) \(7-x^2-y^2-2\left(x+y\right)\)
\(=7-x^2-y^2-2x-2y\)
\(=-\left(x^2+2x+1\right)-\left(y^2+2y+1\right)+9\)
\(=-\left(x+1\right)^2-\left(y+1\right)^2+9\le9\forall x;y\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+1=0\\y+1=0\end{matrix}\right.\) \(\Leftrightarrow x=y=-1\)
Vậy Max của b/t trên là : \(9\Leftrightarrow x=y=-1\)
a )x2+2y2-2xy+2x-4y+2=0
<=>x2-2x(y-1)+y2-2y+1+y2-2y+1=0
<=>x2-2x(y-1)+(y-1)2+(y-1)2=0
<=>(x-y+1)2+(y-1)2=0
<=>x-y+1=0 va y-1=0
<=>x=y-1 y=1
<=>x=1-1=0 y=1
1a/ z2 - 6z + 5 - t2 - 4t = z2 - 2 . 3z + 32 - 4 - t2 - 4t = (z2 - 2 . 3z + 32) - (22 + 2 . 2t + t2) = (z - 3)2 - (2 + t)2
b/ x2 - 2xy + 2y2 + 2y2 + 1 = x2 - 2xy + y2 + y2 + 2y + 1 = (x2 - 2xy + y2) + (y2 + 2y + 1) = (x - y)2 + (y + 1)2
c/ 4x2 - 12x - y2 + 2y + 8 = (2x)2 - 12x - y2 + 2y + 32 - 1 = [ (2x)2 - 2 . 3 . 2x + 32 ] - (y2 - 2y + 1) = (2x - 3)2 - (y - 1)2
2a/ (x + y + 4)(x + y - 4) = x2 + xy - 4x + xy + y2 - 4y + 4x + 4y + 16 = x2 + (xy + xy) + (-4x + 4x) + (-4y + 4y) + y2 + 16
= x2 + 2xy + y2 + 42 = (x + y)2 + 42
b/ (x - y + 6)(x + y - 6) = x2 + xy - 6x - xy - y2 + 6y + 6x + 6y - 36 = x2 + (xy - xy) + (-6x + 6x) + (6y + 6y) - y2 - 36
= x2 - y2 + 12y - 62 = x2 - (y2 - 12y + 62) = x2 - (y2 - 2 . 6y + 62) = x2 - (y - 6)2
c/ (y + 2z - 3)(y - 2z - 3) = y2 -2yz - 3y + 2yz - 4z2 - 6z - 3y + 6z + 9 = y2 + (-2yz + 2yz) + (-3y - 3y) + (-6z + 6z) - 4z2 + 9
= y2 - 6y - 4z2 + 9 = (y2 - 6y + 9) - 4z2 = (y - 3)2 - (2z)2
d/ (x + 2y + 3z)(2y + 3z - x) = 2xy + 3xz - x2 + 4y2 + 6yz - 2xy + 6yz + 9z2 - 3xz = (2xy - 2xy) + (3xz - 3xz) - x2 + (6yz + 6yz) + 9z2 + 4y2
= -x2 + 4y2 + 12yz + 9z2 = (4y2 + 12yz + 9z2) - x2 = [ (2y)2 + 2 . 2 . 3yz + (3z)2 ] - x2 = (2y + 3z)2 - x2
a) x2 - 4x + y2 - 6y + 13
= ( x2 - 4x + 4 ) + ( y2 - 6y + 9 )
= ( x - 2 )2 + ( y - 3 )2
b) x2 - 2xy + 2y2 + 2y + 1
= ( x2 - 2xy + y2 ) + ( y2 + 2y + 1 )
= ( x - y )2 + ( y + 1 )2
c) 4x2 - 12x - y2 + 2y + 8
= ( 4x2 - 12x + 9 ) - ( y2 - 2y + 1 )
= ( 2x - 3 )2 - ( y - 1 )2
= [ ( 2x - 3 ) - ( y - 1 ) ][ ( 2x - 3 ) + ( y - 1 ) ]
= ( 2x - 3 - y + 1 )( 2x - 3 + y - 1 )
= ( 2x - y - 2 )( 2x + y - 4 )
d) x2 + y2 + z2 - 6x - 4y - 2z + 14
= ( x2 - 6x + 9 ) + ( y2 - 4y + 4 ) + ( z2 - 2z + 1 )
= ( x - 3 )2 + ( y - 2 )2 + ( z - 1 )2
Băng Băng 2k6 giúp mik câu mới đăng vs