\(-A=2x^2-0,5x+8\)
=> \(-2A=4x^2-x+16\)
=> \(-2A=\left(2x-\frac{1}{4}\right)^2+\frac{255}{16}\)
Có: \(\left(2x-\frac{1}{4}\right)^2\ge0\)
=> \(-2A\ge\frac{255}{16}\)
=> \(A\le-\frac{255}{16}:2\)
=> \(A\le-\frac{255}{32}\)
DẤU "=" XẢY RA <=> \(\left(2x-\frac{1}{4}\right)^2=0\)
<=> \(x=\frac{1}{8}\)
Tìm GTNN
A= 2a2+b2-2ab=10a+42
Tìm GTLN
A= -x2-y2+2x-6x+9
Tìm gTLNA=\(-x^4+2x^2+4x+2002\)
gtnn,gtlnA=4-6x-x^2
B=3x^2-6x+1
C=5x^2-2x-3
Bài 1tìm GTLN
A=-(2x-5)^2+6|2x-5|+4
B=-x^2-y^2+2x-6y+9
Bài 2
Cho x-y=2, tính giá trị A= 2(x^3-y^3)-3(x+y)^2
tìm GTLN
a)\(A=x^2+5y^2+2xy-4x-8y+2015\)
b)\(B=\left(x-2012\right)^2+\left(x+2013\right)^2\)
c)\(C=\left(x-1\right)\left(2x-1\right)\left(2x^2-3x-1\right)+2017\)
d)\(D=\left(x-1\right)\left(x-3\right)\left(x-4\right)\left(x-6\right)+10\)
Giải PT
1 ) (2x + 1)(3x – 2) = (5x – 8)(2x + 1)
2) 4x2 -1 = (2x + 1)(3x – 5)
3) (x + 1)2 = 4(x2 – 2x + 1)
4) 2x3+ 5x2 – 3x = 0
5) {2x{ = 3x – 2
6) x + 15 = 3x – 1
7) 2 – x = 0,5x – 4
Tìm GTNN
a) A=9x^2+5y^2-5x+3y
Tìm GTLN
a) A= -4x^2-5y^2+8xy+10y+12
b) B= -3x^2-16y^2-8xy-5x+2
. Tìm x, biết:
a) 6x.(x – 5) + 3x.(7 – 2x) = 18 b) 2x.(3x + 1) + (4 – 2x).3x = 7 c) 0,5x.(0,4 – 4x) + (2x + 5).x = -6,5 | d) (x + 3)(x + 2) – (x - 2)(x + 5) = 6 e) 3(2x - 1)(3x - 1) – (2x - 3)(9x - 1) = 0 |
Tìm giá trị nhỏ nhất :
a) A= (0,5x^2+x)^2 - 3 I 0,5x^2+x I
b) B= (x-1)(x-3)( x^2 - 4x +5 )
c) C= x^4 -2x^3 +3x^2 -2x +1
d) D= x^4 - 6x^3 +10x^2 -6x +9
e) E= I x^2 - x +1 I + I x^2 - x -2 I
