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Ta có: \(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\)
\(=\sqrt{\left(9-\sqrt{17}\right)\left(9+\sqrt{17}\right)}\)
\(=\sqrt{81-17}=\sqrt{64}=8\)
1)
ĐK: \(x\geq 2\)
\(\sqrt{x-2}-3\sqrt{x^2-4}=0\)
\(\Leftrightarrow \sqrt{x-2}-3\sqrt{(x-2)(x+2)}=0\)
\(\Leftrightarrow \sqrt{x-2}(1-3\sqrt{x+2})=0\)
\(\Rightarrow \left[\begin{matrix} \sqrt{x-2}=0\\ \sqrt{x+2}=\frac{1}{3}\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=2\\ x=\frac{-17}{9}(\text{loại vì x}\geq 2)\end{matrix}\right.\)
Vậy $x=2$ là nghiệm của pt
2) ĐK: \(x\geq 1\)
Ta có: \(x+\sqrt{x-1}=13\)
\(\Leftrightarrow (x-1)+\sqrt{x-1}+\frac{1}{4}=\frac{49}{4}\)
\(\Leftrightarrow (\sqrt{x-1}+\frac{1}{2})^2=\frac{49}{4}\)
Vì \(\sqrt{x-1}+\frac{1}{2}>0\) nên \(\sqrt{x-1}+\frac{1}{2}=\sqrt{\frac{49}{4}}=\frac{7}{2}\)
\(\Rightarrow \sqrt{x-1}=3\)
\(\Rightarrow x=3^2+1=10\) (thỏa mãn)
Vậy.......
Ta có:
\(x^3=6+3x.\sqrt[3]{9-8}\Leftrightarrow x^3-3x=6\)
\(y^3=34+3y\sqrt[3]{17^2-12^2.2}\Leftrightarrow y^3-3y=34\)
=>B = 6 + 34 + 2017 =2057
Ta có:
x3=6+3x.3√9−8⇔x3−3x=6
y3=34+3y3√172−122.2⇔y3−3y=34
Nên ta suy ra được => B = 6 + 34 + 2017 =2057
Chúc bạn học tốt :)))
Cách 1 :\(A=\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)
\(=\sqrt{\sqrt{5}^2-2\sqrt{5}+\sqrt{1}^2}-\sqrt{\sqrt{5}^2+2\sqrt{5}+\sqrt{1}^2}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{1}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{1}\right)^2}\)
\(=|\sqrt{5}-\sqrt{1}|-|\sqrt{5}+\sqrt{1}|=\sqrt{5}-\sqrt{1}-\sqrt{5}-\sqrt{1}=-2\)
Cách 2 \(A=\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)
\(< =>A^2=6-2\sqrt{5}-6-2\sqrt{5}+2\sqrt{36-20}\)
\(< =>A^2=8-2\sqrt{5}-2\sqrt{5}=8-2\left(2\sqrt{5}\right)=8-4\sqrt{5}\)
<=>...
\(B=\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
\(=\frac{\sqrt{2}-\sqrt{1}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{2}+\sqrt{1}}{\sqrt{17+12\sqrt{2}}}\)
\(=\frac{\left(\sqrt{2}-\sqrt{1}\right)\sqrt{17+12\sqrt{2}}-\left(\sqrt{2}+1\right)\sqrt{17-12\sqrt{2}}}{\sqrt{17^2-\left(12\sqrt{2}\right)^2}}\)
tự làm tiếp đi , mình lười viết
P = \(\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)
P = \(\frac{2\sqrt{x}-9-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)+\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
P = \(\frac{2\sqrt{x}-9-x+9+2x-3\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
P = \(\frac{x-\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
P = \(\frac{x-2\sqrt{x}+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
P = \(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
P = \(\frac{\sqrt{x}+1}{\sqrt{x}-3}\)
Với \(x=6-2\sqrt{5}=5-2\sqrt{5}+1=\left(\sqrt{5}-1\right)^2\)
=> P = \(\frac{\sqrt{\left(\sqrt{5}-1\right)^2}+1}{\sqrt{\left(\sqrt{5}-1\right)^2}-3}=\frac{\sqrt{5}-1+1}{\sqrt{5}-1-3}=\frac{\sqrt{5}}{\sqrt{5}-4}=\frac{\sqrt{5}\left(\sqrt{5}+4\right)}{\left(\sqrt{5}-4\right)\left(\sqrt{5}+4\right)}=\frac{5+4\sqrt{5}}{-11}\)
a: \(B=\dfrac{x-4\sqrt{x}+4\sqrt{x}+16}{x-4}\cdot\dfrac{\sqrt{x}+2}{x+16}=\dfrac{1}{\sqrt{x}-2}\)
b: Khi x=9 thì B=1/(3-2)=1
Đặt \(A=\sqrt{9+\sqrt{17}}-\sqrt{9-\sqrt{17}}\)
\(\Leftrightarrow A^2=18-2\sqrt{\left(9+\sqrt{17}\right)\left(9-\sqrt{17}\right)}\)
\(=18-2\sqrt{81-17}=2\)
\(\Rightarrow A=\sqrt{2}\)
\(\Rightarrow C=A-\sqrt{2}=0\)