ĐKXĐ: \(x\ge\frac{3}{2}\)
\(\Leftrightarrow x^2-\frac{7}{4}+3x-2\sqrt{2x-3}=0\)
\(\Leftrightarrow x^2-\frac{7}{4}+\frac{9x^2-8x+12}{3x+2\sqrt{2x-3}}=0\)
\(\Leftrightarrow x^2-\frac{7}{4}+\frac{9\left(x-\frac{4}{9}\right)^2+\frac{92}{9}}{3x+2\sqrt{2x-3}}=0\)
Do \(x\ge\frac{3}{2}\Rightarrow x^2-\frac{7}{4}>0\Rightarrow VT>0\)
Pt vô nghiệm
tìm điều kiện xác định của biểu thức:
\(a)\frac{6x}{-\sqrt{x+7}}-\frac{3}{-5x-4}+\frac{\sqrt{x}}{-3x+2}\)
\(b)\frac{5-\sqrt{x}}{x+4}+\frac{\sqrt{x-2}-3}{-2x-10}\)
\(c)\frac{\sqrt{6x}}{-x-3}-\frac{4x}{2x+3}\)
\(d)\frac{\sqrt{2x-7}}{3x-4}-\frac{\sqrt{6x}}{x-3}+3x-1\)
Gpt \(\sqrt{1-x}\left(x-3x^2\right)=x^3-3x^2+2x+6\)
Giải phương trình
1) \(3x^2+6x-\frac{4}{3}=\sqrt{\frac{x+7}{3}}\)
2) \(9x^2-x-4=2\sqrt{x+3}\)
3) \(x^2+\sqrt{x+5}=5\)
4) \(2x^2+2x+1=\left(4x-1\right).\sqrt{x^2+1}\)
5) \(x\sqrt{x^2-x+1}+2\sqrt{3x+1}=x^2+x+3\)
\(\sqrt{7-\frac{1}{5}x}\) 2) \(\sqrt{\frac{4}{3}+2x}\)
\(\sqrt{\frac{2}{x^2+\frac{1}{2}}}\) 4) \(\sqrt{\frac{-2}{x^2+\frac{1}{3}}}\)
\(\sqrt{\frac{-5}{x^2+4x}}\) 6) \(\sqrt{\frac{5}{x^2+4x}}\)
\(\sqrt{\frac{2}{x^2+3x-4}}\) 8)\(\sqrt{\frac{2}{3x^2+5x-8}}\)
\(\sqrt{\frac{-6}{x^2-25}}\) 10)\(\sqrt{\frac{-7}{4x^2-9}}\)
\(\sqrt{\frac{2}{4x^2+x+3}}\) Gỉai phương trình
Giúp mk vs các bn mk bí rồi.
Giải phương trình
\(2\sqrt{\frac{3x-1}{x}}=\frac{x}{3x-1}+1\)
\(3\sqrt{\frac{2x}{x-1}}+4\sqrt{\frac{x-1}{2x}}=3.\frac{x-1}{2x}+10\)
GPT
\(2x^2+x+\sqrt{x^2+3}+2x\sqrt{x^2+3}\)
GPT: x4 - 6x + 1 = 2(x + 4)\(\sqrt{2x^3+8x^2+6x+1}\)
Giải phương trình:
a, \(\sqrt{2x^2-9x+4}+3\sqrt{2x-1}=\sqrt{2x^2+21x-11}\)
b, \(\sqrt{1-x}+\sqrt{x^2-3x+2}+\left(x-2\right)\sqrt{\frac{x-1}{x-2}=3}\)
Rút gọn
a) \(3\sqrt{3x-4}+2\left|4-3x\right|-2=0\)
b)\(\sqrt{x^2+2x+1}+\sqrt{x^2-4x+4}=3\)
c)\(\sqrt{4x^2+4x\sqrt{7}+7}-\sqrt{8-2\sqrt{7}}=0\)
