2Q=\(2x-4\sqrt{2x-1}\)
2Q=\(\left(2x-1\right)-4\sqrt{2x-1}+4-3\)
Q=\(\dfrac{\left(\sqrt{2x-1}-2\right)^2-3}{2}\ge\dfrac{-3}{2}\forall x\in R\)
Dấu = xảy ra khi \(\sqrt{2x-1}-2=0\Leftrightarrow x=\dfrac{5}{2}\)
vậy \(Q_{min}=\dfrac{-3}{2}khi\) x\(=\dfrac{5}{2}\)
\(\sqrt{x^2-2x+4}+1\)
tim gtnn
Tìm x:
a) \(\sqrt{x+\sqrt{2x-1}}\) + \(\sqrt{x-2\sqrt{2x-1}}\) =\(\sqrt{2}\)
b) \(\sqrt{x+2+3\sqrt{2x-5}}\) + \(\sqrt{x-2-\sqrt{2x-5}}\) = \(2\sqrt{2}\)
giải pt
a)\(\sqrt{\dfrac{2x-3}{x-1}}=2\)
b)\(\dfrac{\sqrt{2x-3}}{\sqrt{x-1}}=2\)
c)\(\sqrt{4x^2-9}=2\sqrt{2x+3}\)
d)\(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)
e)\(\sqrt{4x-20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
Tìm \(x\) biết :
a) \(\sqrt{x-5}=3\)
b) \(\sqrt{x-10}=-2\)
c) \(\sqrt{2x-1}=\sqrt{5}\)
d) \(\sqrt{4-5x}=12\)
\(\sqrt{2x^2+x+9}+\sqrt{2x^2-x+1}=x+4\)
1) Tìm số thực x,y,z thõa mãn điều kiện :
\(\sqrt{x}\) + \(\sqrt{y-1}\)+ \(\sqrt{z-2}\) = \(\dfrac{1}{2}\)(x+y+z)
2) Giai phương trình : a) \(\sqrt{3x^2-6x+4}\)+\(\sqrt{2x^2-4x+6}\)=2+2x-x2
b) \(\sqrt{3x^2+6x+12}\)+\(\sqrt{5x^4-10x^2+9}\) =3-4x-2x2
Rút gọn các biểu thức sau:
\(\sqrt{x+2\sqrt{x-1}}\)
\(\sqrt{x-1-2\sqrt{x-2}}\)
\(\sqrt{x-2+2\sqrt{x-3}}-\sqrt{x-3}\)
\(\sqrt{2x-2\sqrt{x^2-4}}+\sqrt{x-2}\)
bài 1:tìm x biết
a) \(\sqrt{2x-1}=5\) c) \(\sqrt{x^2-6x+9}=5\)
b) \(\sqrt{4\left(x-1\right)}=12\)
bài 2: tìm x biết căn thức có nghĩa
a) \(\sqrt{2x-\dfrac{1}{3}}\) b) \(\sqrt{5-3x}\)
c) \(\sqrt{\dfrac{x+1}{5-x}}\) d) \(\sqrt{x^2-5x-6}\)
BÀI 1 : THỰC HIỆN PHÉP TÍNH
a, \(\left(1+\sqrt{3}-\sqrt[2]{2}\right)\times\left(1+\sqrt{3}+\sqrt[2]{2}\right)\)
b, \(\left(\dfrac{3}{2}\times\sqrt{6}+2\times\sqrt{\dfrac{2}{3}}-4\times\sqrt{\dfrac{3}{2}}\right)\times\left(3\times\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
BÀI 2 : rút gọn
B = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-2}}\)