ĐK:x\(\ge-1\)
\(\sqrt{7+\sqrt{2+\sqrt{x+1}}}=3\Leftrightarrow7+\sqrt{2+\sqrt{x+1}}=9\Leftrightarrow\sqrt{2+\sqrt{x+1}}=2\Leftrightarrow2+\sqrt{x+1}=4\Leftrightarrow\sqrt{x+1}=2\Leftrightarrow x+1=4\Leftrightarrow x=3\left(tm\right)\)
Vậy S={3}
cho \(P=\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{9x-1}\right)\div\left(1-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\)
1, rút gọn P
2, tìm x để \(P\ge0\)
tính P khi \(x=-\sqrt{3-2\sqrt{2}}+\dfrac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}\)
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. \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
P=\(\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{3-11\sqrt{x}}{9-x}\)
1. Tính P khi x=\(7+2\sqrt{3}\)
2. Tìm x để P<1
(\(\frac{3x+\sqrt{16x}-7}{x+2\sqrt{x}-3}\)-\(\frac{\sqrt{x}+1}{\sqrt{x}+3}\)-\(\frac{\sqrt{x}+7}{\sqrt{x}-1}\))/(2-\(\frac{\sqrt{x}}{\sqrt{x}-1}\))
Cho \(\sqrt{x-3}-\sqrt[3]{y^2+5y+7}=\sqrt{y-1}-\sqrt[3]{x^2+x+1}\)
Cho biểu thức A=\(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
Rút gọn A?
b, Tính A biết x=\(\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}+\sqrt{83-18\sqrt{2}}\)
Giải phương trình
a, \(x+1+2\sqrt{7-x}-2\sqrt{x+1}=\sqrt{7+6x-x^2}\)
b, \(4x^2+3x+3=4\sqrt{x^3+3x^2}+2\sqrt{2x-1}\)
c, \(\sqrt{x}-\sqrt{x+1}-\sqrt{x+4}+\sqrt{x+9}=0\)
d, \(3x^2+4x+10=2\sqrt{14x^2-7}\)
cho \(x=\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
\(y=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
tính giá trị bt: \(A=\dfrac{xy-1}{x+y}-\dfrac{1-xy}{2x-y}\)
rút gọn
\(\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{7\sqrt{x}+3}{9-x}\)
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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