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3x^2 + 6x - 1
= 3(x^2 + 2x - 1/3)
= 3(x^2 + 2x + 1 - 4/3)
= 3(x+1)^2 - 4 ≥ - 4
=> Cmin = - 4
Dấu "=" xảy ra khi x + 1 = 0<=> x = -1
Vậy Cmin = -4 khi x = -1
3x^2 + 6x - 1
= 3(x^2 + 2x - 1/3)
= 3(x^2 + 2x + 1 - 4/3)
= 3(x+1)^2 - 4 ≥ - 4
=> min = - 4
Dấu "=" xảy ra khi x + 1 = 0<=> x = -1
Vậy min = -4 khi x = -1
![](https://rs.olm.vn/images/avt/0.png?1311)
9 x 2 - 6 x + 1 ≠ 0 ⇒ 3 x - 1 2 ≠ 0 ⇒ x ≠ 1 / 3 ta có x = - 8 ≠ 1/3
Thay x = - 8 vào biểu thức, ta có:
![](https://rs.olm.vn/images/avt/0.png?1311)
A = x2 + 5x + 7
= ( x2 + 5x + 25/4 ) + 3/4
= ( x + 5/2 )2 + 3/4
\(\left(x+\frac{5}{2}\right)^2\ge0\forall x\Rightarrow\left(x+\frac{5}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)
Đẳng thức xảy ra <=> x + 5/2 = 0 => x = -5/2
=> MinA = 3/4 <=> x = -5/2
B = 6x - x2 - 5
= -( x2 - 6x + 9 ) + 4
= -( x - 3 )2 + 4
\(-\left(x-3\right)^2\le0\forall x\Rightarrow-\left(x-3\right)^2+4\le4\)
Đẳng thức xảy ra <=> x - 3 = 0 => x = 3
=> MaxB = 4 <=> x = 3
C = ( x - 1 )( x + 2 )( x + 3 )( x + 6 )
= [ ( x - 1 )( x + 6 ) ][ ( x + 2 )( x + 3 ) ]
= [ x2 + 5x - 6 ][ x2 + 5x + 6 ]
= ( x2 + 5x )2 - 36
\(\left(x^2+5x\right)^2\ge0\forall x\Rightarrow\left(x^2+5x\right)^2-36\ge-36\)
Đẳng thức xảy ra <=> x2 + 5x = 0
<=> x( x + 5 ) = 0
<=> x = 0 hoặc x = -5
=> MinC = -36 <=> x = 0 hoặc x = -5
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=x^2-6x+10\)
\(\Leftrightarrow A=x^2-2\cdot x\cdot3+3^2-9+10\)
\(\Leftrightarrow A=\left(x-3\right)^2+1\ge1\) \(\forall x\in z\)
\(\Leftrightarrow A_{min}=1khix=3\)
\(B=3x^2-12x+1\)
\(\Leftrightarrow B=\left(\sqrt{3}x\right)^2-2\cdot\sqrt{3}x\cdot2\sqrt{3}+\left(2\sqrt{3}\right)^2-12+1\)
\(\Leftrightarrow B=\left(\sqrt{3}x-2\sqrt{3}\right)^2-11\ge-11\) \(\forall x\in z\)
\(\Leftrightarrow B_{min}=-11khix=2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1:
a: A=x^2+4x+4+13
=(x+2)^2+13>=13
Dấu = xảy ra khi x=-2
b; =x^2-8x+16+84
=(x-4)^2+84>=84
Dấu = xảy ra khi x=4
c: =x^2+x+1/4+19/4
=(x+1/2)^2+19/4>=19/4
Dấu = xảy ra khi x=-1/2
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) x≠2
Bài 2:
a) x≠0;x≠5
b) x2−10x+25x2−5x=(x−5)2x(x−5)=x−5x
c) Để phân thức có giá trị nguyên thì x−5x phải có giá trị nguyên.
=> x=−5
Bài 3:
a) (x+12x−2+3x2−1−x+32x+2)⋅(4x2−45)
=(x+12(x−1)+3(x−1)(x+1)−x+32(x+1))⋅2(2x2−2)5
=(x+1)2+6−(x−1)(x+3)2(x−1)(x+1)⋅2⋅2(x2−1)5
=(x+1)2+6−(x2+3x−x−3)(x−1)(x+1)⋅2(x−1)(x+1)5
=[(x+1)2+6−(x2+2x−3)]⋅25
=[(x+1)2+6−x2−2x+3]⋅25
=[(x+1)2+9−x2−2x]⋅25
=2(x+1)25+185−25x2−45x
=2(x2+2x+1)5+185−25x2−45x
=2x2+4x+25+185−25x2−45x
=2x2+4x+2+185−25x2−45x
=2x2+4x+205−25x2−45x
c) tự làm, đkxđ: x≠1;x≠−1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=-3x^2+6x-7=-3\left(x^2-2x+1-1\right)-7\)
\(=-3\left(x-1\right)^2-4\le-4\)Dấu ''='' xảy ra khi x = 1
\(B=-2x^2+5x+1=-2\left(x^2-\dfrac{5}{2}x\right)+1\)
\(=-2\left(x^2-2.\dfrac{5}{4}x+\dfrac{25}{16}-\dfrac{25}{16}\right)+1\)
\(=-2\left(x-\dfrac{5}{4}\right)^2+\dfrac{33}{8}\le\dfrac{33}{8}\)Dấu ''='' xảy ra khi x = 5/4
C;D chỉ có GTNN thôi bạn nhé \(C=2x^2-8x+13=2\left(x^2-4x+4-4\right)+13\)
\(=2\left(x-2\right)^2+5\ge5\)Dấu ''='' xảy ra khi x = 2
\(D=x^2-3x+5=x^2-2.\dfrac{3}{2}x+\dfrac{9}{4}-\dfrac{9}{4}+5\)
\(=\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\)Dấu ''='' xảy ra khi x = 3/2
d: Ta có: \(D=x^2-3x+5\)
\(=x^2-2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{11}{4}\)
\(=\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{3}{2}\)
Bài làm:
Ta có: \(C=3x^2-6x-1\)
\(C=3\left(x^2-2x-\frac{1}{3}\right)\)
\(C=3\left(x^2-2x+1\right)-4\)
\(C=3\left(x-1\right)^2-4\ge-4\left(\forall x\right)\)
Dấu "=" xảy ra khi: \(3\left(x-1\right)^2=0\Rightarrow x=1\)
Vậy \(Min_C=-4\Leftrightarrow x=1\)
C = 3x2 - 6x - 1
= 3( x2 - 2x + 1 ) - 4
= 3( x - 1 )2 - 4
\(3\left(x-1\right)^2\ge0x\Rightarrow\forall3\left(x-1\right)^2-4\ge-4\)
Đẳng thức xảy ra <=> x - 1 = 0 => x = 1
=> MinC = -4 <=> x = 1