Đặt \(\sqrt{2x-\dfrac{5}{x}}=a;\sqrt{x-\dfrac{1}{x}}=b\)(a,b>=0)
Ta có \(a^2-b^2=2x-\dfrac{5}{x}-x+\dfrac{1}{x}=x-\dfrac{4}{x}\)
Ta có pt \(\Leftrightarrow a-b=a^2-b^2\Leftrightarrow\left(a-b\right)\left(a+b-1\right)=0\Leftrightarrow\left[{}\begin{matrix}a=b\\a+b=1\end{matrix}\right.\)
rút gọn:
\(A=\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{2}\)
\(B=\dfrac{2x}{x+3\sqrt{x}+2}+\dfrac{5\sqrt{x}+1}{x+4\sqrt{x}-3}+\dfrac{\sqrt{x}+10}{x+5\sqrt{x}+6}\)
Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
1) \(\dfrac{x-3x^2}{2}+\sqrt{2x^4-x^3+7x^2-3x+3}=2\)
2) \(1+\sqrt{\dfrac{x-2}{1-x}}=\dfrac{2x^2-2x+1}{x^2-2x+2}\)
3) \(x+y+z+\dfrac{3}{x-1}+\dfrac{3}{y-1}+\dfrac{3}{z-1}=2\left(\sqrt{x+2}+\sqrt{y+2}+\sqrt{z+2}\right)\) với x ,y ,z > 1
4) \(\sqrt[3]{x+6}+x^2=7-\sqrt{x-1}\)
5) \(x^4-2x^3+x-\sqrt{2\left(x^2-x\right)}=0\)
Giai phuong trinh
1/ \(\sqrt{x-3}+\sqrt{2-x}=5\)
2/ \(2x+7\sqrt{x}+\dfrac{7}{\sqrt{x}}+\dfrac{2}{x}+9=0\)
3/ \(x+\dfrac{1}{x}-4\sqrt{x}-\dfrac{4}{\sqrt{x}}+6=0\)
4/ \(\sqrt{x+9}=5-\sqrt{x-2}\)
Giải các phương trình sau:
1. \(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)\)
2. \(x^2+4x+7=\left(x+4\right)\sqrt{x^2+7}\)
3. \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
4. \(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
5. \(x=\left(\sqrt{x}+2\right)\left(1-\sqrt{1-\sqrt{x}}\right)\)
6. \(2\sqrt[3]{2x-1}=x^3+1\)
7. \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
Rút gọn: \(F=\left(\dfrac{2x\sqrt{x}+x-\sqrt{x}}{x\sqrt{x}-1}-\dfrac{x+\sqrt{x}}{x-1}\right)\cdot\dfrac{x-1}{2x+\sqrt{x}-1}+\dfrac{\sqrt{x}}{2x-1}\)
giải hệ phương trình
\(\left\{{}\begin{matrix}\sqrt{x-2}+\sqrt{y-3}=3\\2\sqrt{x-2}-3\sqrt{y-3}=-4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}+\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=4\end{matrix}\right.\)
1, \(\sqrt{x+1}-\sqrt{\dfrac{x-1}{x}}=1\)
2, \(\sqrt{x^2-\dfrac{7}{x}}+\sqrt{x-\dfrac{7}{x^2}}=x\)
3, \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
4, \(x=\left(\sqrt{x}+2\right)\left(1-\sqrt{1-\sqrt{x}}\right)^2\)
5, \(2\sqrt[3]{2x-1}=x^3+1\)
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Rút gọn: \(Q=\left(\dfrac{\sqrt{x}+1}{\sqrt{x-2}}-\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{5\sqrt{x}+2}{4-x}\right):\dfrac{3\sqrt{x}-x}{x+4\sqrt{x}+4}\). Tìm các giá trị nguyên của x để Q âm
