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20 tháng 6 2018

Giải:

\(-x^2-2x-2\)

\(=-x^2-2x-1-1\)

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

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

\(\Leftrightarrow x+1=0\Leftrightarrow x=-1\)

Vậy ...

2) \(-4x^2+12x+10\)

\(=-4x^2+12x-9+19\)

\(=-\left(4x^2-12x+9\right)+19\)

\(=-\left(2x-3\right)^2+19\)

\(=19-\left(2x-3\right)^2\le19\)

\(\Leftrightarrow2x-3=0\Leftrightarrow x=\dfrac{3}{2}\)

Vậy ...

3) \(-x^2-4x\)

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

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

\(=-\left(x+2\right)^2+4\le4\)

\(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

Vậy ...

4) \(-x^2+6x-5\)

\(=-x^2+6x-9+4\)

\(=-\left(x^2-6x+9\right)+4\)

\(=-\left(x-3\right)^2+4\le4\)

\(\Leftrightarrow x-3=0\Leftrightarrow x=3\)

Vậy ...

1: \(=-\left(x^2+2x+2\right)=-\left(x^2+2x+1+1\right)=-\left(x+1\right)^2-1< =-1\)

Dấu '=' xảy ra khi x=-1

2: \(=-\left(4x^2-12x-10\right)\)

\(=-\left(4x^2-12x+9-19\right)\)

\(=-\left(2x-3\right)^2+19< =19\)

Dấu '=' xảy ra khi x=3/2

3: \(=-\left(x^2+4x+4-4\right)=-\left(x+2\right)^2+4< =4\)

Dấu '=' xảy ra khi x=-2

20 tháng 6 2018

Những hằng đẳng thức đáng nhớ

20 tháng 6 2018

Giải:

5) \(-x^2+x-\dfrac{1}{2}\)

\(=-x^2+x-\dfrac{1}{4}+\dfrac{3}{4}\)

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

\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\le\dfrac{3}{4}\)

\(\Leftrightarrow x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{2}\)

Vậy ...

6) \(-\dfrac{1}{4}x^2+x-2\)

\(=-\dfrac{1}{4}x^2+x-1-1\)

\(=-\left(\dfrac{1}{4}x^2-x+1\right)-1\)

\(=-\left(\dfrac{1}{2}x-1\right)^2-1\le-1\)

\(\Leftrightarrow\dfrac{1}{2}x-1=0\Leftrightarrow x=2\)

Vậy ...

7) \(-\dfrac{1}{9}x^2-\dfrac{1}{3}x+1\)

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

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

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

\(\Leftrightarrow\dfrac{1}{3}x+\dfrac{1}{2}=0\Leftrightarrow x=-\dfrac{3}{2}\)

Vậy ...

8) \(-2x^2+2xy-2y^2+2x+2y-8\)

\(=-x^2+2xy-y^2+2x-x^2+2y-y^2-1-1-6\)

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

\(=-\left(x-y\right)^2-\left(x-1\right)^2-\left(y-1\right)^2-6\le-6\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\x-1=0\\y-1=0\end{matrix}\right.\Leftrightarrow x=y=1\)

Vậy ...

26 tháng 5 2018

cảm ơn bn nhiều!!!!

20 tháng 6 2018

méo hiểu đề bạn à

26 tháng 5 2018

4. 4x2 + 4x + 1 = ( 2x + 1)2

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

\(=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)^2\)

6. \(4a^2-\dfrac{4}{3}ab+\dfrac{1}{9}b^2=\left(2a\right)^2-2.2a.\dfrac{1}{3}+\left(\dfrac{1}{3}b\right)^2=\left(2a-\dfrac{1}{3}b\right)^2\)

7.

\(9x^2+4xy+\dfrac{4}{9}y^2-25z^2=\left(3x+\dfrac{2}{3}y\right)^2-\left(5z\right)^2=\left(3x+\dfrac{2}{3}y-5z\right)\left(3x+\dfrac{2}{3}y+5z\right)\)

26 tháng 5 2018

x2 - 6x + 9 = (x-3)2

x2 - 2x + 1 - y2 = ( x-1)2 - y2 = ( x-1-y)(x-1+y)

4x2 +12xy +9y2 = ( 2x+3y)2

30 tháng 8 2017

x^2 -6x +10 = x^2 -2.x.3 +3^2 +1 = (x-3)^2 +1 
Ma (x-3)^2 >=0 <=> (x-3)^2 +1 >=1>0 (voi moi x) 
b) 4x - x^2 -5 = -(x^2 -4x +5) =-[(x^2 -4x +4)+1] = -[(x-2)^2 +1] 
Ma (x+2)^2 >=0 <=> (x-2)^2 +1 >=1 <=> -[(x-2)^2 +1] <=-1 => -[(x-2)^2 +1] <0 
2) a) P= x^2 -2x +5 = x^2 -2x +1 +4 = (x-1)^2 +4 
Ta co: (x-1)^2 >=0 <=> (x-1)^2 +4 >=4 
Vay gia tri nho nhat P=4 khi x=1 
b) Q= 2x^2 -6x = 2(x^2 -3x) = 2(x^2 - 2.x.3/2 + 9/4 -9/4)= 2[(x-3/2)^2 -9/4] 
Ta co: (x-3/2)^2 >=0 <=>(x-3/2)^2 -9/4 >= -9/4 <=> 2[(x-3/2)^2 -9/4] >= -9/2 
Vay gia tri nho nhat Q= -9/2 khi x= 3/2 
c) M= x^2 +y^2 -x +6y +10 = (x^2 -2.x.1/2 + 1/4) +(y^2 +2.y.3+9)+3/4 
= ( x-1/2)^2 + (y+3)^2 +3/4 
M>= 3/4 
Vay GTNN cua M = 3/4 khi x=1/2 va y=-3 
3)a) A= 4x - x^2 +3 = -(x^2 -4x -3) = -( x^2 -4x+4 -7) =-[(x-2)^2 -7] 
Ta co: (x-2)^2>=0 <=> (x-2)^2 -7 >=-7 <=> -[(x-2)^2 -7] <=7 
Vay GTLN A=7 khi x=2 
b) B= x-x^2 = -(x^2 -2.x.1/2+1/4-1/4) = -[(x-1/2)^2 -1/4] 
GTLN B= 1/4 khi x=1/2 
c) N= 2x - 2x^2 -5 =-2( x^2 -x+5/2) = -2(x^2 - 2.x.1/2 +1/4 +9/4) 
= -2[(x-1/2)^2 +9/4] 
GTLN N= -9/2 khi x=1/2

26 tháng 5 2018

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

26 tháng 5 2018

bạn ơi bạn có thể giải thick cách lm đc ko