ĐKXĐ: \(x\ge11\)
\(\Leftrightarrow2x+2\sqrt{x^2-x+11}=16\)
\(\Leftrightarrow\sqrt{x^2-x+11}=8-x\)
Do \(x\ge11\Rightarrow8-x< 0\Rightarrow\left\{{}\begin{matrix}VT>0\\VP< 0\end{matrix}\right.\)
Phương trình vô nghiệm
Phương trình chứa căn
Các câu hỏi tương tự
a)\(\sqrt{4x-1}+\sqrt{4x^2-1}=1\)
b)\(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\)
c)\(\sqrt{x}-x=1-\sqrt{2x+1}\)
d)\(\sqrt{x}+\sqrt{4-x}-2=-x\)
e)\(\sqrt{4+x}+x=\sqrt{4+12x}\)
Giai pt
1,sqrt{x+8-6sqrt{x-1}}4
2,sqrt{x+6-2sqrt{x+2}}+sqrt{x+11-6sqrt{x+2}}1
3,sqrt{x-3-2sqrt{x-4}}+sqrt{x-4sqrt{x-4}}1
4,sqrt{x-2+sqrt{2x+5}}+sqrt{x+2+3sqrt{2x-5}}dfrac{7}{2}
5,sqrt{2x+4+6sqrt{2x-5}}+sqrt{2x-4-2sqrt{2x-5}}4
6,sqrt{dfrac{1}{4}x^2+x+1}-sqrt{6-2sqrt{5}}0
7,x+sqrt{x+dfrac{1}{2}}+sqrt{x+dfrac{1}{4}}2
8,sqrt{left(x-1right)+4-4sqrt{x-1}}+sqrt{x-1-6sqrt{x-1+9}}1
9,sqrt{x+2sqrt{x-1}}+sqrt{x-2sqrt{x-1}}dfrac{x+3}{2}
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Giai pt
1,\(\sqrt{x+8-6\sqrt{x-1}}\)=4
2,\(\sqrt{x+6-2\sqrt{x+2}}\)+\(\sqrt{x+11-6\sqrt{x+2}}\)=1
3,\(\sqrt{x-3-2\sqrt{x-4}}\)+\(\sqrt{x-4\sqrt{x-4}}\)=1
4,\(\sqrt{x-2+\sqrt{2x+5}}\)+\(\sqrt{x+2+3\sqrt{2x-5}}\)=\(\dfrac{7}{2}\)
5,\(\sqrt{2x+4+6\sqrt{2x-5}}\)+\(\sqrt{2x-4-2\sqrt{2x-5}}\)=4
6,\(\sqrt{\dfrac{1}{4}x^2+x+1}\)-\(\sqrt{6-2\sqrt{5}}\)=0
7,x+\(\sqrt{x+\dfrac{1}{2}}\)+\(\sqrt{x+\dfrac{1}{4}}\)=2
8,\(\sqrt{\left(x-1\right)+4-4\sqrt{x-1}}+\sqrt{x-1-6\sqrt{x-1+9}}\)=1
9,\(\sqrt{x+2\sqrt{x-1}}\)+\(\sqrt{x-2\sqrt{x-1}}\)=\(\dfrac{x+3}{2}\)
Giải giúp mih phương trình này đi mà............
a, x2-6x+9=\(4\sqrt{x^2-6x+6}\)
b, x2+\(\sqrt{x^2+11}\) =31
Giải các phương trình sau:1) sqrt{3x^2+5x+8}-sqrt{3x^2+5x+1}12) x^2-2x-12+4sqrt{left(4-xright)left(2+xright)}03) 3sqrt{x}+dfrac{3}{2sqrt{x}}2x+dfrac{1}{2x}-74) sqrt{x}-dfrac{4}{sqrt{x+2}}+sqrt{x+2}05)left(x-7right)sqrt{dfrac{x+3}{x-7}}x+46) 2sqrt{x-4}+sqrt{x-1}sqrt{2x-3}+sqrt{4x-16}7) sqrt{x+2sqrt{x-1}}+sqrt{x-2sqrt{x-1}}dfrac{x+3}{2}Giúp mình với ajk, mink đang cần gấp
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Giải các phương trình sau:
1) \(\sqrt{3x^2+5x+8}-\sqrt{3x^2+5x+1}=1\)
2) \(x^2-2x-12+4\sqrt{\left(4-x\right)\left(2+x\right)}=0\)
3) \(3\sqrt{x}+\dfrac{3}{2\sqrt{x}}=2x+\dfrac{1}{2x}-7\)
4) \(\sqrt{x}-\dfrac{4}{\sqrt{x+2}}+\sqrt{x+2}=0\)
5)\(\left(x-7\right)\sqrt{\dfrac{x+3}{x-7}}=x+4\)
6) \(2\sqrt{x-4}+\sqrt{x-1}=\sqrt{2x-3}+\sqrt{4x-16}\)
7) \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\dfrac{x+3}{2}\)
Giúp mình với ajk, mink đang cần gấp
Tìm x:
a.\(\sqrt{4-\sqrt{4+x}}=x\)
b.\(4\left(\sqrt{x-1}-3\right)x^2+\left(13\sqrt{x+1}-8\right)x-4\sqrt{x-1}-3=0\)
c.\(\sqrt{2x-3}+2\sqrt{x-3}\ge3\sqrt[4]{2x^2+x-6}\)
rut gon P=(\(\frac{3\sqrt{x}}{\sqrt{x}+2}+\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{x-\sqrt{x}}{x-4}\)):\(\left(\frac{3\sqrt{x}}{\sqrt{x}+2}\right)\)
Giải phương trình:
1. \(x\sqrt{x}+\dfrac{32}{x\sqrt{x}}=6\sqrt[3]{3x-4}\)
2. \(\sqrt{x^2+x-1}+\sqrt{-x^2+x+1}=x^2-x+2\)
3. \(\sqrt{8-x^2}+\sqrt{\dfrac{x^2-2}{2x^2}}=5-\dfrac{1+x^2}{x}\)
4. \(x^4-12x^3+38x^2-12x-67+\sqrt{x+1}+\sqrt{7-x}=0\)
Giải phương trình:
1) \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
2) \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
1, \(x^3-x-3=2\sqrt{6x-x^2}\)
2, \(x^3+6x^2-171x-40\left(x+1\right)\sqrt{5x-1}+20=0\)
3, \(\sqrt[3]{x+3}+\sqrt[3]{x-3}=\sqrt[5]{x-5}+\sqrt[5]{x+5}\)
4. \(\left(\frac{1}{\sqrt{x}}-\frac{\sqrt{x}}{x+1}\right)^2=\frac{4\left(1+\sqrt{1+4x}\right)}{x+1+\sqrt{x^2+3x+2}}\)