ĐKXĐ: ...
\(\Leftrightarrow x^2-x+2\left(x+1-\sqrt{3x+1}\right)+\sqrt{x+2}-\sqrt{1+\sqrt{3x+1}}=0\)
\(\Leftrightarrow x^2-x+\frac{2\left(x^2-x\right)}{x+1+\sqrt{3x+1}}+\frac{x+1-\sqrt{3x+1}}{\sqrt{x+2}+\sqrt{1+\sqrt{3x+1}}}=0\)
\(\Leftrightarrow x^2-x+\frac{2\left(x^2-x\right)}{x+1+\sqrt{3x+1}}+\frac{x^2-x}{\left(\sqrt{x+2}+\sqrt{1+\sqrt{3x+1}}\right)\left(x+1+\sqrt{3x+1}\right)}=0\)
\(\Leftrightarrow x^2-x=0\)
\(\Leftrightarrow...\)
Giải pt sau:
a. \(\sqrt{2x^2-3x-11}=\sqrt{x^2-1}\)
b. \(\sqrt{2x^2+3x-5}=x+1\)
c. \(\sqrt{\left(x+2\right)^2}=\sqrt{3x^2-5x+14}\)
d. \(\sqrt{\left(x-1\right)\cdot\left(2x-3\right)}=-x-9\)
GPT : x = \(\sqrt{2-x}\cdot\sqrt{3-x}+\sqrt{3-x}\cdot\sqrt{5-x}+\sqrt{5-x}\cdot\sqrt{2-x}\)
Giải phương trình:
\(\sqrt{4-x^2}+6=2\sqrt{2+x}+3\sqrt{2-x}\\ \left(\sqrt{2-x}+1\right)^2=3x+1\)
1. Rút gọn \(A=\frac{\sqrt{14+6\sqrt{5}}-\sqrt{14-6\sqrt{5}}}{\sqrt{\left(\sqrt{5}+1\right)\cdot\sqrt{6-2\sqrt{5}}}}\)
2.Tính a) \(B=\left(\sqrt[3]{2}+1\right)^3\cdot\left(\sqrt[3]{2}-1\right)^3\)
b)Tìm C=\(a^3b-ab^3\) với \(a=\frac{6}{2\sqrt[3]{2}-2+\sqrt[3]{4}}\); \(b=\frac{2}{2\sqrt[3]{2}+2+\sqrt[3]{4}}\)
3. Giải \(\left|x^2-x+1\right|-\left|x-2\right|=6\)
Giải phương trình: \(x^2-2x-1=\sqrt{\left(x^2+1\right)\cdot\left(x+1\right)}\)
\(\left(\sqrt{2-x}+1\right)\cdot\left(\sqrt{x+3}-\sqrt{x-1}\right)=4\)
giải phương trình sau \(2x^3-2x+\sqrt{2x^3-3x+1}=3x+1+\sqrt[3]{x^2+2}\)
giải phương trình \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\frac{x+3}{2}\)
g=\(\left(\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}}{x+2\sqrt{x}+1}\right)\cdot\dfrac{x^2-2x+1}{2}\)
Giải phương trình
a) \(\left(\sqrt{1+x}+\sqrt{1-x}\right)\left(2+2\sqrt{1-x^2}\right)=8\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
