ĐKXĐ: ...
\(\Leftrightarrow x+3-x+2\sqrt{x\left(3-x\right)}=3\)
\(\Leftrightarrow\sqrt{x\left(3-x\right)}=0\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
b/ \(2sin^2x-5sinx+2=0\)
\(\Leftrightarrow\left(2sinx-1\right)\left(sinx-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=\frac{1}{2}\\sinx=2\left(l\right)\end{matrix}\right.\) \(\Rightarrow cosx=\sqrt{1-sin^2x}=\frac{\sqrt{3}}{2}\)
\(\Rightarrow sinx.cosx=\frac{\sqrt{3}}{4}\)
Giải pt:
\(a)x^{4}-2\sqrt{2}x^{2}+2=\sqrt{2}+x \\b)(2x+3)\sqrt{x^{2}-2}=2x^{2}+3x-4 \\c)2x^{2}+2(x+1)\sqrt{x^{2}-1}-6x+1=0\)
Giải pt sau :
\(x^2-3x+1+\dfrac{\sqrt{3}}{3}.\sqrt{x^4+x^2+1}=0\)
Bài 1: giải các PT sau
a) \(2\sqrt{x}=6\)
b) \(4-5\sqrt{x}=-1\)
c) \(4\sqrt{x}=-3\)
d) \(\sqrt{x}\left(\sqrt{x}-2\right)=0\)
e) \(\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)=0\)
f) \(\left(\sqrt{x}+\sqrt{2}\right)\left(\sqrt{x}+3\right)=0\)
Bài 2:
\(9\left(x+2\right)^2-108=0\)
Bài 1: Giải PT
a) \(\sqrt{x^2-1}-x^2+1=0\)
b) \(\sqrt{x^2-4}-x+2=0\)
c) \(\sqrt{x^4-8x^2+16}=2-x\)
d) \(\sqrt{9x^2+6x+1}\sqrt{11-6\sqrt{2}}\)
e) \(\sqrt{4^2-9}=2\sqrt{2x+3}\)
f) \(\sqrt{4x-20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
Giải pt: \(\dfrac{3\sqrt{x}-5}{2}-\dfrac{2\sqrt{x}-7}{3}=\sqrt{x}-1\)
giải pt: \(x^2+x-17=\sqrt{\left(x^2-15\right)\left(x-3\right)}+\sqrt{x^2-15}+\sqrt{x-3}\)
giải hệ pt sau
\(\left\{{}\begin{matrix}y^3+\sqrt{8x^4-2y}=2\left(2x^4+3\right)\\\sqrt{2x^2+x+y}+2\sqrt{x+2y}=\sqrt{9x-2x^2+19y}\end{matrix}\right.\)
giải pt
`a,(x+\sqrt{3})+4(x^2-3)=0`
Giải các pt sau:
1, \(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
2, \(\sqrt{x}+\sqrt{x+\sqrt{1-x}=1}\)
3, \(\sqrt{1-\sqrt{x^2-x}=\sqrt{x}-1}\)