\(\left|5x-2\right|+\left|5x\right|=\left|2-5x\right|+\left|5x\right|\)
Áp dụng bđt \(\left|A\right|+\left|B\right|\ge\left|A+B\right|\)
\(\left|2-5x\right|+\left|5x\right|\ge\left|2-5x+5x\right|=\left|2\right|=2\)
Dấu "$=$" xảy ra khi \(\left(2-5x\right)\cdot5x\ge0\Leftrightarrow0\le x\le\dfrac{2}{5}\)
Tim gtnn cua bieu thuc
C=5x^2-7x+4
D=x^2+y^2-2x-4y-6
Tìm x để BT đc xác định:
\(\sqrt{5x^2+4x+7}\)
1. Tim GTNN cua bieu thuc:
\(A=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)
2. Rut gon bieu thuc:
a) \(A=\sqrt{29-4\sqrt{7}}+\sqrt{23+8\sqrt{7}}\)
b)\(B=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}},voix>=2\)
Giúp mình nhé!!
2. Rut gon bieu thuc:
a) \(A=\sqrt{x-2+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}},voix>=3\)
3. Tim GTNN cua bieu thuc:
a) \(A=\sqrt{4x^2-12x+9}+\sqrt{x^2-10x+25}+\sqrt{9x^2-6x+1}+\sqrt{16x^2-72x+81}\)
b) \(B=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)
Tìm GTNN:
A=\(\sqrt{25-10x+x^2}-\sqrt{x^2-6x+9}\)
B:\(\dfrac{1}{2x^2-x+3}\)
C: x2 - 2xy + 3y2 - 2x + 2017
D: x-\(\sqrt{x-2015}\)
E:\(\dfrac{2x+1}{x^2}\)
F: \(\dfrac{5x^2-4x+4}{x^2}\)
G=(x+1)(x+2)2(x+3)
H= X2-5x+y2+xy-4y+2014
I= x2 +xy +y2-3x-3y +2002
K=\(\sqrt{x^2-6x+2y^2+4y+11}+\sqrt{x^2+2x+3y^2+6y+4}\)
\(x^2-5x+8-2\sqrt{x-2}=0\)
\(\sqrt{5x^2+4x+7}\)
Giải các phương trình sau :
a) \(\sqrt{x-1}+\sqrt{x-4}=\sqrt{x+4}\)
b) \(\sqrt[3]{2x-1}+\sqrt[3]{x-1}=1\)
c) \(5\sqrt{x^2+5x+8}=x^2+5x+4\)
Gải phương trình: \(\sqrt{x-2}+\sqrt{4-x}=2x^2-5x-1\)
