giải phương trình ( liên hợp ) e đang cần gấp cảm ơn
1) \(\sqrt{3x+4}\)-\(\sqrt{5-x}\)=-3x2+8x+9
2)(\(\sqrt{x+2}\)-\(\sqrt{x-1}\))(\(\sqrt{2-x}\)+1)=1
3) \(\sqrt{x^2-x+1}\)+\(\sqrt{x^2-9x+9}\)=2x
4)\(\sqrt[3]{2x+1}\)+\(\sqrt[3]{x}\)=1
5)\(\sqrt{3x+1}\)-\(\sqrt{6-x}\)+3x2-14x=8
6) (\(\sqrt{x+4}\)-2)\(\left(\sqrt{4-x}+2\right)\)=2x
1.
Bạn coi lại đề
2.
ĐKXĐ: \(1\le x\le2\)
Nhận thấy \(\sqrt{x+2}+\sqrt{x-1}>0;\forall x\) , nhân 2 vế của pt với nó:
\(\left(\sqrt{x+2}+\sqrt{x-1}\right)\left(\sqrt{x+2}-\sqrt{x-1}\right)\left(\sqrt{2-x}+1\right)=\sqrt{x+2}+\sqrt{x-1}\)
\(\Leftrightarrow3\left(\sqrt{2-x}+1\right)=\sqrt{x+2}+\sqrt{x-1}\)
\(\Leftrightarrow3\sqrt{2-x}+3=\sqrt{x+2}+\sqrt{x-1}\)
\(\Leftrightarrow3\sqrt{2-x}+2-\sqrt{x+2}+1-\sqrt{x-1}=0\)
\(\Leftrightarrow3\sqrt{2-x}+\frac{2-x}{2+\sqrt{x+2}}+\frac{2-x}{1+\sqrt{x-1}}=0\)
\(\Leftrightarrow\sqrt{2-x}\left(3+\frac{\sqrt{2-x}}{2+\sqrt{x+2}}+\frac{\sqrt{2-x}}{1+\sqrt{x-1}}\right)=0\)
\(\Leftrightarrow\sqrt{2-x}=0\Rightarrow x=2\)
5.
ĐKXĐ: ...
\(\Leftrightarrow3x^2-14x-5+\sqrt{3x+1}-4+1-\sqrt{6-x}=0\)
\(\Leftrightarrow\left(3x+1\right)\left(x-5\right)+\frac{3\left(x-5\right)}{\sqrt{3x+1}+4}+\frac{x-5}{1+\sqrt{6-x}}=0\)
\(\Leftrightarrow\left(x-5\right)\left(3x+1+\frac{3}{\sqrt{3x+1}+4}+\frac{1}{1+\sqrt{6-x}}\right)=0\)
\(\Leftrightarrow x=5\)
6.
ĐKXĐ: \(-4\le x\le4\)
\(\Leftrightarrow\frac{\left(\sqrt{x+4}-2\right)\left(\sqrt{x+4}+2\right)\left(\sqrt{4-x}+2\right)}{\sqrt{x+4}+2}=2x\)
\(\Leftrightarrow\frac{x\left(\sqrt{4-x}+2\right)}{\sqrt{x+4}+2}=2x\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\frac{\sqrt{4-x}+2}{\sqrt{x+4}+2}=2\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow\sqrt{4-x}+2=2\sqrt{x+4}+4\)
\(\Leftrightarrow2\sqrt{x+4}-\frac{4}{5}+\frac{14}{5}-\sqrt{4-x}=0\)
\(\Leftrightarrow\frac{2\left(x+4-\frac{4}{25}\right)}{\sqrt{x+4}+\frac{2}{5}}+\frac{\frac{196}{25}-4+x}{\frac{14}{5}+\sqrt{4-x}}=0\)
\(\Leftrightarrow\left(x-\frac{96}{25}\right)\left(\frac{2}{\sqrt{x+4}+\frac{2}{5}}+\frac{1}{\frac{14}{5}+\sqrt{4-x}}\right)=0\)
\(\Rightarrow x=\frac{96}{25}\)
3.
ĐKXĐ: ...
\(\Leftrightarrow x-\sqrt{x^2-x+1}+x-\sqrt{x^2-9x+9}=0\)
\(\Leftrightarrow\frac{x-1}{x+\sqrt{x^2-x+1}}+\frac{9\left(x-1\right)}{x+\sqrt{x^2-9x+9}}=0\)
\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{x+\sqrt{x^2-x+1}}+\frac{9}{x+\sqrt{x^2-9x+9}}\right)=0\)
\(\Leftrightarrow x=1\)
4.
\(\Leftrightarrow\sqrt[3]{2x+1}-1+\sqrt[3]{x}=0\)
\(\Leftrightarrow\frac{2x}{\sqrt[3]{\left(2x+1\right)^2}+\sqrt[3]{2x+1}+1}+\sqrt[3]{x}=0\)
\(\Leftrightarrow\sqrt[3]{x}\left(\frac{2\sqrt[3]{x^2}}{\sqrt[3]{\left(2x+1\right)^2}+\sqrt[3]{2x+1}+1}+1\right)=0\)
\(\Leftrightarrow x=0\)
