\(x^2-3x+1=\dfrac{5\sqrt{3}}{3}\sqrt{x^4+x^2+1}\)
\(\Leftrightarrow\)\(\left(x^2-3x+1\right)^2=\dfrac{25}{3}\left(x^4+x^2+1\right)\)
\(\Leftrightarrow\)\(x^4-6x^3+11x^2-6x+1=\dfrac{25}{3}x^4+\dfrac{25}{3}x^2+\dfrac{25}{3}\)
\(\Leftrightarrow11x^4+9x^3-4x^2+9x+11=0\)
\(\Leftrightarrow\left(x+1\right)\left(11x^3-2x^2-2x+11\right)=0\)
\(\Rightarrow x=-1\)
Giải các pt sau:
a) \(\sqrt{\dfrac{x+1}{x+3}}+\sqrt{x+1}=\sqrt{x^2-x+1}+\sqrt{x+3}\)
b) \(\sqrt{x^2+12}+5=3x+\sqrt{x^2+5}\)
1)giải pt: 1+\(\dfrac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
2)giải pt: \(\dfrac{x^2}{\sqrt{3x-2}}-\sqrt{3x-2}=1-x\)
Tính và rút gọn:
C=\(\dfrac{2}{\sqrt{5}+1}+\sqrt{\dfrac{2}{3-\sqrt{5}}}\)
Giai các pt sau:
\(\sqrt{3x+1}-\sqrt{x-1}\)=2
b, \(\sqrt{x-5}\)=x-7
giải pt : \(\dfrac{1}{\sqrt{x+1}+\sqrt{x+2}}+\dfrac{1}{\sqrt{x+2}+\sqrt{x+3}}+\dfrac{1}{\sqrt{x+3}+\sqrt{x+4}}+...+\dfrac{1}{\sqrt{x+2019}+\sqrt{x+2020}}=11\)
bài 1
a) \(\sqrt{2X+1}\)
b)\(\sqrt{x^2-4}\)
c) \(\dfrac{3}{\sqrt{3X+5}}\)
d) \(\sqrt{X-3}-\sqrt{10-x}\)
e) \(\sqrt{x+4}+\dfrac{2-X}{x^2-16}\)
(*) tìm x để căn thức sau có nghĩa:
\(a,\sqrt{2x-1}\\ b,\sqrt{\dfrac{3}{x+1}}\\ c,\sqrt{3x^2}\\ d,\sqrt{\dfrac{3}{x^2}}\\ e,\sqrt{-\dfrac{1}{x^2+2}}\\ f,\sqrt{\dfrac{2}{3}x-\dfrac{1}{5}}\)
Gải pt:
a) \(\sqrt{x+5}+\sqrt{3-x}-2\left(\sqrt{15-2x-x^2}+1\right)=0\)
b) \(3\sqrt{3}\left(x^2+4x+2\right)-\sqrt{x+8}=0\)
c) \(x^2-x-2\sqrt{1+16x}=2\)
Giải:
1)a) \(17\sqrt{3x-1}=3x\)
b) \(\sqrt{2+\sqrt{3x-5}}=\sqrt{x+1}\)
c)\(\sqrt{\dfrac{5x+7}{x+3}}=4\)
2)Giai pt :
a) x+y+12=\(4\sqrt{x}+6\sqrt{y}-1\)
b) \(\sqrt{x-a}+\sqrt{y-b}+\sqrt{z-c}=\dfrac{1}{2}\left(x+y+z\right)\)
c)\(\sqrt{x+\sqrt{14x-4y}}+\sqrt{x-\sqrt{14x-4y}}=\sqrt{14}\)
d)x-\(4\sqrt{2x+2}-2\sqrt{2-x+9}=0\)
giải các phương trình
1) \(\sqrt{4x-20}\) +3\(\sqrt{\dfrac{x-5}{9}}\) \(-\dfrac{1}{3}\sqrt{9x-45}=6\)
2)\(\sqrt{x+1}+\sqrt{x+6}=5\)
3) \(x^2-6x+\sqrt{x^2-6x+7}=5\)
4)\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=4\)
5)\(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)\)
6)\(\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
7)\(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2\)