Tim Min : m^2 - 6m + x ^ 2 - x +3
b) 3x^2 -6x +12
Tìm
Min A= 3x^2+2x+7/x^2+2x+3
Max B= 2x^2-16x+29/x^2-6x+10
Min C = 6x^2-14x+29/x^2-2x+5
Max D = 5x^2+2x+2/x^2+x+1
Tìm MIN, MAX
A=x^2-4x+10
B=(1-x).(3x+4)
C=3x^2-9x+5
D= - 2x^2+5x+2
E=-3x^2-6x+5
F=x^4-2x^2+3
G=(x^2+2)^2-3
H=x^2+y^2-6x+4y+12
tim x biet
a/(3x-5)(2x-1)-(x+2)(6x-1)=0
b/ (3x-5)(3x+2)-(3x-1)2=-5
c/(3x+2)(x-5)=3(x-1)2-2
d/ (x+1)2/3 - (x-2)2/2 = 2x+1/2 (x-3)2/6
g/49x2=(3x+2)2
h/(3x-4)2-(2x-2)2-3(x-2)(2x-1)=0
i/ (x-2)(x2-2x+4)-x(x2+2)=15
k/ 6x2-7x-3=0
m/(x+5)(x-3)+x2-25=0
e/ x3+3x2=4x+12
f/ (6x+7)2(3x+4)(x+1)=6
Tìm min:
A= x2+6x+5
B= (x-1).(x-3)
C= x2-x+8
D= x2-3x
\(A=x^2+6x+5=\left(x^2+6x+9\right)-4=\left(x+3\right)^2-4\ge-4\)
Vậy \(MIN_A=-4\) khi \(\left(x+3\right)^2=0\Leftrightarrow x=-3\)
\(B=\left(x-1\right)\left(x-3\right)=x^2-4x+3=\left(x^2-4x+4\right)-1=\left(x-2\right)^2-1\ge-1\)
Vậy \(MIN_B=-1\) khi \(\left(x-2\right)^2=0\Leftrightarrow x=2\)
\(C=x^2-x+8=\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{31}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{31}{4}\ge\dfrac{31}{4}\)
Vậy \(MIN_C=\dfrac{31}{4}\) khi \(\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x=\dfrac{1}{2}\)
\(D=x^2-3x=\left(x^2-3x+\dfrac{9}{4}\right)-\dfrac{9}{4}=\left(x-\dfrac{3}{2}\right)^2-\dfrac{9}{4}\ge-\dfrac{9}{4}\)
Vậy \(MIN_D=-\dfrac{9}{4}\) khi \(\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x=\dfrac{1}{2}\)
Cho M = -2 x(3X^3 - 4X^2 +7X-6+(6X^3-8X^2+7X--4-3x)
tim X bt M = 0
1. tìm Min , Max
a, A= x^2-1+1
b,B= 3x^2-5+7
c,C= -2x^2 - x +1
d= x^2 +y^2 -2x +6y +12
e, E= -2x^2 +x
f= x^2+5y^2 - 4xy +6x -14y+15
đề câu a, b có sai ko vậy pn,mk thấy sai
phân tích thành nhân tử
1.-3x^4y-6x^3y^2-3x^2y^3
2. 4a^2 - x^2- 2x- 1
3. m^2- 6m+ 9 - x^2 + 4xy - 4y^2
Tìm min
F=3x^2 +x -2
G= 4x^2+2x-1
H=5x^2-x+1
Tìm max
A= -x^2 -6x+3
B=-x^2+8x-1
C= -x^2-3X+4
D= -2x^2+3x-1
E= -3x^2 – x +2
F= -5x^2 -4x +3
G= -3x^2 – 5x+1
Tìm min:
$F=3x^2+x-2=3(x^2+\frac{x}{3})-2$
$=3[x^2+\frac{x}{3}+(\frac{1}{6})^2]-\frac{25}{12}$
$=3(x+\frac{1}{6})^2-\frac{25}{12}\geq \frac{-25}{12}$
Vậy $F_{\min}=\frac{-25}{12}$. Giá trị này đạt tại $x+\frac{1}{6}=0$
$\Leftrightarrow x=\frac{-1}{6}$
Tìm min
$G=4x^2+2x-1=(2x)^2+2.2x.\frac{1}{2}+(\frac{1}{2})^2-\frac{5}{4}$
$=(2x+\frac{1}{2})^2-\frac{5}{4}\geq 0-\frac{5}{4}=\frac{-5}{4}$ (do $(2x+\frac{1}{2})^2\geq 0$ với mọi $x$)
Vậy $G_{\min}=\frac{-5}{4}$. Giá trị này đạt tại $2x+\frac{1}{2}=0$
$\Leftrightarrow x=\frac{-1}{4}$
Tìm min
$H=5x^2-x+1=5(x^2-\frac{x}{5})+1$
$=5[x^2-\frac{x}{5}+(\frac{1}{10})^2]+\frac{19}{20}$
$=5(x-\frac{1}{10})^2+\frac{19}{20}\geq \frac{19}{20}$
Vậy $H_{\min}=\frac{19}{20}$. Giá trị này đạt tại $x-\frac{1}{10}=0$
$\Leftrightarrow x=\frac{1}{10}$
Tìm min của
A=\(x-x^2\)
\(B=3x^2-6x+12\)
tìm max của
\(C=6x-3x^2\)
ai làm đc tick cho@@@@
\(A=x-x^2\)
\(A=-\left(x^2-x\right)\)
\(A=-\left(x^2-2\cdot x\cdot\frac{1}{2}+\frac{1}{4}-\frac{1}{4}\right)\)
\(A=-\left[\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\right]\)
\(A=\frac{1}{4}-\left(x-\frac{1}{2}\right)^2\le\frac{1}{4}\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x=\frac{1}{2}\)
Còn lại tương tự
\(C=6x-3x^2\)
\(C=-3\left(x^2-2x\right)\)
\(C=-3\left(x^2-2x+1-1\right)\)
\(C=-3\left[\left(x-1\right)^2-1\right]\)
\(C=-3\left(x-1\right)^2+3\le3\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x=1\)