tìm GTLN,GTNN của:
\(\left(x-1\right)\left(x+5\right)\left(x^2+4x+5\right)\)
tìm GTLN,GTNN của: A = \(\left(x-1\right)\left(x+5\right)\left(x^2+4x+5\right)\)
Câu 1: Rút gọn các biểu thức sau:
1. \(\left(x+y-z\right)^2+\left(y-z\right)^2+2z\left(z-y\right)\)
2. \(\left(3x+4\right)^2+\left(x-4\right)^2+2\left(3x+4\right)\left(x-4\right)\)
3.\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
4. \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)\)
5. \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
Câu 2: Tìm x
1. \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=1\)
2. \(\left(3x+1\right)^2+\left(5x-2\right)^2=34\left(x+2\right)\left(x-2\right)\)
3. \(\left(x+3\right)^2+\left(x-2\right)^2=2x^2\)
4. \(4x^2-9-x\left(2x-3\right)=0\)
5. \(4x^2-12x+9=0\)
Câu 3: Tìm GTNN
D = \(\left(2x-1\right)^2+\left(x+2\right)^2\)
Câu 4: Cho \(a^2+b^2+c^2=ab+bc+ac\) . Chứng minh rằng a=b=c
Tìm x, biết :
a/ \(\dfrac{1}{3}x\left(x^2-4\right)=0\)
b/ \(x\left(x+5\right)=x+5\)
c/ \(x^3-\dfrac{1}{9}x=0\)
3)\(^2-\left(x+5\right)^2=0\)
e/ \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
f/ \(x\left(2x-3\right)-6+4x=0\)
g/ \(2\left(3x-2\right)^2-9x^2+4=0\)
h/ \(x^2\left(x+1\right)+2x\left(x+1\right)=0\)
i/ \(4x^2+9x+5=0\)
Tìm GTNN của biểu thức sau
C=\(\left(2x-1\right)^2+\left(x+2\right)^2\)
D =\(2x^2+6x-5\)
E = \(\left(x+2\right).\left(x+3\right).\left(x+4\right).\left(x+5\right)\)
Bài 1: Tìm GTNN của biểu thức:
\(A=x^2+3x+7\)
\(B=2x^2-8x\)
\(C=x^2-4x+y^2-8y+6\)
\(D=\left(x+1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)\)
Bài 2: Tìm GTLN của biểu thức:
\(A=11-10x-x^2\)
\(B=-3x\left(x+3\right)-7\)
\(C=5-x^2+2x-4y^2-4y\)
\(D=\left|x-4\right|\left(2-\left|x-4\right|\right)\)
Tìm GTNN của: C= x + \(\dfrac{1}{4x}\)+ \(\dfrac{x}{\left(2x+1\right)^{ }2}\)
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)\(D=\left(x-1\right)\left(x-3\right)\left(x-4\right)\left(x-6\right)+10\)
BÀI 6 tìm x
1,\(2x\left(x-5\right)-\left(3x+2x^2\right)=0\) 2,\(x\left(5-2x\right)+2x\left(x-1\right)=13\)
3,\(2x^3\left(2x-3\right)-x^2\left(4x^2-6x+2\right)=0\) 4,\(5x\left(x-1\right)-\left(x+2\right)\left(5x-7\right)=6\)
5,\(6x^2-\left(2x-3\right)\left(3x+2\right)=1\) 6,\(2x\left(1-x\right)+5=9-2x^2\)
