ĐKXĐ: ...
\(E=x-2005-\sqrt{x-2005}+\frac{1}{4}+\frac{8019}{4}\)
\(E=\left(\sqrt{x-2005}-\frac{1}{2}\right)^2+\frac{8019}{4}\ge\frac{8019}{4}\)
\(E_{min}=\frac{8019}{4}\) khi \(x=\frac{8021}{4}\)
\(F=\sqrt{\left(2-x\right)^2}+\sqrt{\left(x+5\right)^2}\)
\(F=\left|2-x\right|+\left|x+5\right|\ge\left|2-x+x+5\right|=7\)
\(F_{min}=7\) khi \(-5\le x\le2\)
tìm x:
\(\sqrt{x^2+x+1}=1\)
\(\sqrt{x^2+1}=-3\)
\(\sqrt{x^2-10x+25}=7-2x\)
\(\sqrt{2x+5}=5\)
\(\sqrt{x^2-4x+4}-2x+5=0\)
Giải các pt sau:\(\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=3\)
\(\sqrt{x^2-10x+25}=3-19x\)
\(\sqrt{2x-2+2\sqrt{2x-3}}+\sqrt{2x+13+8\sqrt{2x-3}}=5\)
giai phuong trinh \(\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=\sqrt{1+2005^2+\dfrac{2005^2}{2006^2}}+\dfrac{2005}{2006}\)
Tìm x
\(\sqrt{x-2+2\sqrt{ }x-3}\) + \(\sqrt{x+6+6+\sqrt{x-3}}\)
Tìm GTNN
a) \(\sqrt{9x^2-6x+1}\) + \(\sqrt{25-30x+9x^2}\)
b) \(\sqrt{x^2-6x+1}\) + \(\sqrt{x^2+10x+25}\)
Giải phương trình sau:
a)\(\sqrt{\left(x-3\right)^2}=3-x\) b)\(\sqrt{4x^2-20x+25}+2x=5\)
c)\(\sqrt{1-12x+36x^2}=5\) d)\(\sqrt{x+2\sqrt{x-1}}=2\)
e)\(\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}-1\) f)\(\sqrt{x^2-\dfrac{1}{2}x+\dfrac{1}{16}}=\dfrac{1}{4}-x\)
Mọi người giúp em với!!!!
Bài 2
a) A= \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(-2\right)^6}-\sqrt{\left(1+\sqrt{2}\right)^2}\)
b) B= \(\sqrt{7+2\sqrt{6}}+\sqrt{7-2\sqrt{6}}\)
c) C= \(\sqrt{7-4\sqrt{3}}\)
d) D= \(2\sqrt{7+4\sqrt{3}}-\sqrt{13-4\sqrt{3}}\)
e) E= \(\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+...+\frac{1}{\sqrt{79}+\sqrt{81}}\)
Bài 4:
a) \(\sqrt{x-1}=2\)
b) \(\sqrt{x^2-3x+2}=\sqrt{2}\)
c) \(\sqrt{4x+1}=x+1\)
d) \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2\)
e) \(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
f)
Tìm x:
a) \(\left(5x-6\right)^2-\frac{1}{\sqrt{5x-7}}=x^2-\frac{1}{\sqrt{x-1}}\)
b) \(4x^3+x-\left(x+1\right)\sqrt{2x+1}=0\)
c) \(\frac{\sqrt{x+1}-2}{\sqrt[3]{2x+1}-3}=\frac{1}{x+2}\)
d) \(-2x^3+10x^2-17x+8=2x^2\sqrt[3]{5x-x^2}\)
e) \(9x^2-28x+21=\sqrt{x-1}\)
f) \(3x\left(2+\sqrt{9x^2+3}\right)+\left(4x+2\right)\sqrt{1+x+x^2}+1=0\)
Mng giúp em với ạ, em cảm ơn
Tìm x: \(a.\sqrt{4-5x}=12\)
\(b.\sqrt{10+\sqrt{3x}}=2+\sqrt{6}\)
c. \(\sqrt{4x+20}-3\sqrt{5+x}+\frac{4}{3}\sqrt{9x+45}=6\)
d. \(\sqrt{x^2-9}-3\sqrt{x-3}=0\)
e. \(\sqrt{\frac{4x+3}{x+1}}=3\)
f. \(\sqrt{x-2}\le3\)
B1: tính : A = \(\sqrt{7+4\sqrt{3}}\) + \(\sqrt{7-4\sqrt{3}}\)
B2: cho P= 3x-\(\sqrt{x^2-10x+25}\)
a, rút gọn P
b, tính P khi x=2
B3: rút gọn : M = \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\)với x khác 1
giúp em zới ạ 
em cảm mơn nhìu nhìu 