\(=\left(3\sqrt{2}-3+4\sqrt{2}+2-4-2\sqrt{2}\right)\cdot\left(2\sqrt{2}+2\right)\)
\(=\left(5\sqrt{2}-5\right)\left(2\sqrt{2}+2\right)\)
=10
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Ôn tập chương 1: Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
\(\left(\dfrac{3}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{4}{2-\sqrt{2}}\right)\left(\sqrt{8}+2\right)\)
Rút gọn các biểu thức sau :
a) left(sqrt{8}-3sqrt{2}+sqrt{10}right)sqrt{2}-sqrt{5}
b) 0,2sqrt{left(-10right)^2.3}+2sqrt{left(sqrt{3}-sqrt{5}right)^2}
c) left(dfrac{1}{2}sqrt{dfrac{1}{2}}-dfrac{3}{2}sqrt{2}+dfrac{4}{5}sqrt{200}right):dfrac{1}{8}
d) 2sqrt{left(sqrt{2}-3right)^2}+sqrt{2.left(-3right)^2}-5sqrt{left(-1right)^4}
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Rút gọn các biểu thức sau :
a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}\)
b) \(0,2\sqrt{\left(-10\right)^2.3}+2\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}\)
c) \(\left(\dfrac{1}{2}\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{200}\right):\dfrac{1}{8}\)
d) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2.\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}\)
Bài 1: Cho A dfrac{1}{2sqrt{1}+1sqrt{2}}+dfrac{1}{3sqrt{2}+2sqrt{3}}+dfrac{1}{4sqrt{3}+3sqrt{4}}+...+dfrac{1}{100sqrt{99}+99sqrt{100}}
So sánh A với 1
Bài 2: Tính
A left(dfrac{3}{sqrt{2}+1}+dfrac{14}{2sqrt{2}-1}-dfrac{4}{2-sqrt{2}}right).left(sqrt{8}+2right)
Bài 3: Tính tổng
Sdfrac{1}{sqrt{2}+sqrt{3}}+dfrac{1}{sqrt{3}+sqrt{4}}+dfrac{1}{sqrt{4}+sqrt{5}}+...+dfrac{1}{sqrt{2018}+sqrt{2019}}
Đọc tiếp
Bài 1: Cho A = \(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+...+\dfrac{1}{100\sqrt{99}+99\sqrt{100}}\)
So sánh A với 1
Bài 2: Tính
A = \(\left(\dfrac{3}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{4}{2-\sqrt{2}}\right).\left(\sqrt{8}+2\right)\)
Bài 3: Tính tổng
S=\(\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\dfrac{1}{\sqrt{4}+\sqrt{5}}+...+\dfrac{1}{\sqrt{2018}+\sqrt{2019}}\)
câu1 : a) A dfrac{sqrt{15}-sqrt{12}}{sqrt{5}-2}-dfrac{1}{2-sqrt{3}}
b) left(dfrac{sqrt{a}-2}{sqrt{a}+2}-dfrac{sqrt{a}+2}{sqrt{a}-2}right).left(sqrt{a}-dfrac{4}{sqrt{a}}right)
Câu 2 :
a) A left(2sqrt{4+sqrt{6-2sqrt{5}}}right).left(sqrt{10}-sqrt{2}right)
b) B left(dfrac{sqrt{a}-1}{sqrt{a}+1}+dfrac{sqrt{a}+1}{sqrt{a}-1}right).left(1-dfrac{2}{a+1}right)^2
Đọc tiếp
câu1 : a) A= \(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\dfrac{1}{2-\sqrt{3}}\)
b) \(\left(\dfrac{\sqrt{a}-2}{\sqrt{a}+2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-2}\right).\left(\sqrt{a}-\dfrac{4}{\sqrt{a}}\right)\)
Câu 2 :
a) A= \(\left(2\sqrt{4+\sqrt{6-2\sqrt{5}}}\right).\left(\sqrt{10}-\sqrt{2}\right)\)
b) B= \(\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right).\left(1-\dfrac{2}{a+1}\right)^2\)
Dạng 3.Chứng minh đẳng thức
Bài 1: CM
a)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=2\)
b)\(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}=8\)
Bài 2 :CM
\(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{2}}=\sqrt{\sqrt{5}+1}\)
từ giả thiết, ta có dfrac{1}{xy}+dfrac{1}{yz}+dfrac{1}{zx}1
đặt left(dfrac{1}{xy};dfrac{1}{yz};dfrac{1}{zx}right)left(a;b;cright)Rightarrow a+b+c1 left(dfrac{ac}{b};dfrac{ab}{c};dfrac{bc}{a}right)left(dfrac{1}{x^2};dfrac{1}{y^2};dfrac{1}{z^2}right)
ta có VTdfrac{1}{sqrt{1+dfrac{1}{x^2}}}+dfrac{1}{sqrt{1+dfrac{1}{y^2}}}+dfrac{1}{sqrt{1+dfrac{1}{z^1}}}sqrt{dfrac{1}{1+dfrac{ac}{b}}}+sqrt{dfrac{1}{1+dfrac{ab}{c}}}+sqrt{dfrac{1}{1+dfrac{bc}{a}}}
dfrac{1}{sqrt{dfrac{b+ac}{b}}}+dfrac{1}{sqrt{dfrac...
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từ giả thiết, ta có \(\dfrac{1}{xy}+\dfrac{1}{yz}+\dfrac{1}{zx}=1\)
đặt \(\left(\dfrac{1}{xy};\dfrac{1}{yz};\dfrac{1}{zx}\right)=\left(a;b;c\right)\Rightarrow a+b+c=1\) =>\(\left(\dfrac{ac}{b};\dfrac{ab}{c};\dfrac{bc}{a}\right)=\left(\dfrac{1}{x^2};\dfrac{1}{y^2};\dfrac{1}{z^2}\right)\)
ta có VT=\(\dfrac{1}{\sqrt{1+\dfrac{1}{x^2}}}+\dfrac{1}{\sqrt{1+\dfrac{1}{y^2}}}+\dfrac{1}{\sqrt{1+\dfrac{1}{z^1}}}=\sqrt{\dfrac{1}{1+\dfrac{ac}{b}}}+\sqrt{\dfrac{1}{1+\dfrac{ab}{c}}}+\sqrt{\dfrac{1}{1+\dfrac{bc}{a}}}\)
=\(\dfrac{1}{\sqrt{\dfrac{b+ac}{b}}}+\dfrac{1}{\sqrt{\dfrac{a+bc}{a}}}+\dfrac{1}{\sqrt{\dfrac{c+ab}{c}}}=\sqrt{\dfrac{a}{\left(a+b\right)\left(a+c\right)}}+\sqrt{\dfrac{b}{\left(b+c\right)\left(b+a\right)}}+\sqrt{\dfrac{c}{\left(c+a\right)\left(c+b\right)}}\)
\(\le\sqrt{3}\sqrt{\dfrac{ac+ab+bc+ba+ca+cb}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}}=\sqrt{3}.\sqrt{\dfrac{2\left(ab+bc+ca\right)}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}}\)
ta cần chứng minh \(\sqrt{\dfrac{2\left(ab+bc+ca\right)}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}}\le\dfrac{3}{2}\Leftrightarrow\dfrac{2\left(ab+bc+ca\right)}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\le\dfrac{9}{4}\Leftrightarrow8\left(ab+bc+ca\right)\le9\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
<=>\(8\left(a+b+c\right)\left(ab+bc+ca\right)\le9\left(a+b\right)\left(b+c\right)\left(c+a\right)\) (luôn đúng )
^_^
1)Thực hiện phép tính : Adfrac{2}{sqrt{2}}-dfrac{1}{sqrt{3}-sqrt{2}}+dfrac{2}{sqrt{3}-1} Bleft(dfrac{5+2sqrt{6}}{sqrt{3}+sqrt{2}}right)^2-left(dfrac{5-2sqrt{6}}{sqrt{3}-sqrt{2}}right)^2
2)Cho biểu thức : Pleft(dfrac{sqrt{a}}{2}-dfrac{1}{2sqrt{a}}right)^2.left(dfrac{sqrt{a}-1}{sqrt{a}+1}-dfrac{sqrt{a}+1}{sqrt{a}-1}right)
a.Rút gọn...
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1)Thực hiện phép tính : A=\(\dfrac{2}{\sqrt{2}}-\dfrac{1}{\sqrt{3}-\sqrt{2}}+\dfrac{2}{\sqrt{3}-1}\) \(B=\left(\dfrac{5+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\right)^2-\left(\dfrac{5-2\sqrt{6}}{\sqrt{3}-\sqrt{2}}\right)^2\)
2)Cho biểu thức : \(P=\left(\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}}\right)^2.\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}-\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)
a.Rút gọn P
a) \(\sqrt{243}-\dfrac{1}{2}\sqrt{12}-2\sqrt{75}+2\sqrt{27}\)
b) \(\left(2+\sqrt{6}\right)\sqrt{7-4\sqrt{3}}\)
c) \(\sqrt{\dfrac{\sqrt{5}}{8\sqrt{5}+3\sqrt{35}}}.\left(3\sqrt{2}+\sqrt{14}\right)\)
Bài 1 :tính giá trị của biểu thức
a) left(sqrt{5}+sqrt{2}right)left(3sqrt{2}-1right)
b) 3sqrt{50}-2sqrt{75}-4dfrac{sqrt{54}}{sqrt{3}}-3sqrt{dfrac{1}{3}}
c) sqrt{left(sqrt{3}-3right)^2}+sqrt{4+2sqrt{3}}
d) sqrt{48-2sqrt{135}}-sqrt{45}+sqrt{18}
e)dfrac{5sqrt{2}-2sqrt{5}}{sqrt{5}-sqrt{2}}+dfrac{6}{2-sqrt{10}}-dfrac{20}{sqrt{10}}
Bài 2 :Tính:
a) 3sqrt{2x}-5sqrt{8x}+7sqrt{18x}
b) left(2sqrt{3}+4right)left(sqrt{3}-2right)
c) sqrt{3+2sqrt{2}}+sqrt{left(sqrt{2}-2right)^2}
d)sqrt{4-sqrt{15}}-sq...
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Bài 1 :tính giá trị của biểu thức
a) \(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)
b) \(3\sqrt{50}-2\sqrt{75}-4\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
c) \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4+2\sqrt{3}}\)
d) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)
e)\(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
Bài 2 :Tính:
a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)
b) \(\left(2\sqrt{3}+4\right)\left(\sqrt{3}-2\right)\)
c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)
d)\(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)
e)\(\left(\dfrac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\dfrac{4}{1+\sqrt{5}}+4\right)\)
f) \(\dfrac{1}{5}\sqrt{50}-2\sqrt{96}-\dfrac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\dfrac{1}{6}}\)