Các câu hỏi tương tự
\(y=\frac{1}{2+\sqrt{2}}+\frac{1}{3\cdot\sqrt{2}+2\cdot\sqrt{3}}+\frac{1}{4\cdot\sqrt{3}+3\cdot\sqrt{4}}+...+\frac{1}{100\cdot\sqrt{99}+99\cdot\sqrt{100}}\)tính y
Chứng minh: \(\frac{1}{2\cdot\sqrt{1}}+\frac{1}{3\cdot\sqrt{2}}+\frac{1}{4\cdot\sqrt{3}}+...+\frac{1}{2012\cdot\sqrt{2011}}+\frac{1}{2013\cdot\sqrt{2012}}\)\(< 2\)
Chứng minh: A=\(\frac{1}{3\cdot\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\cdot\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\cdot\left(\sqrt{48}+\sqrt{49}\right)}\)\(< \frac{1}{2}\)
1. Tính:
a. \(\text{[}\sqrt{ab}+2\sqrt{\frac{b}{a}}-\sqrt{\frac{a}{b}}+\sqrt{\frac{1}{ab}}\text{]}\cdot\sqrt{ab}\)
b.\(\text{[}-\frac{am}{b}\cdot\sqrt{\frac{n}{m}}-\frac{ab}{n}\cdot\sqrt{mn}+\frac{a^2}{b^2}\cdot\sqrt{\frac{m}{n}}\text{]}\cdot\text{[}a^2b^2\cdot\sqrt{\frac{n}{m}}\text{]}\)
tính: \(\text{[}\sqrt{2}-1\text{]}^2-\frac{3}{2}\cdot\sqrt{\text{[}-2\text{]}^2}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{25}}\cdot\sqrt{2}\)
Chứng minh: \(\sqrt{x}\cdot\text{[}1-\sqrt{x}\text{]}\le\frac{1}{4}v\text{ới}x\ge0\)
1. CHỨNG MINH ĐẲNG THỨCa. text{[}3+2sqrt{6}-sqrt{33}text{]}cdottext{[}sqrt{22}+sqrt{6}+4text{]}24b. text{[}frac{1}{5-2sqrt{6}}+frac{2}{5+2sqrt{6}}text{]}cdottext{[}15+2sqrt{6}text{]}c.text{[}frac{4}{3}cdotsqrt{3}+sqrt{2}+sqrt{3frac{1}{3}}text{]}cdottext{[}sqrt{1,2}+sqrt{2}-4sqrt{frac{1}{5}}text{]}4d. sqrt{text{[}1-sqrt{1989}text{]}^2}cdotsqrt{1990+2sqrt{1989}}1988e. frac{a-sqrt{ab}+b}{asqrt{a}+bsqrt{b}}-frac{1}{a-b}frac{sqrt{a}-sqrt{b}-1}{a-b}với a0;b0và ane b
Đọc tiếp
1. CHỨNG MINH ĐẲNG THỨC
a. \(\text{[}3+2\sqrt{6}-\sqrt{33}\text{]}\cdot\text{[}\sqrt{22}+\sqrt{6}+4\text{]}=24\)
b. \(\text{[}\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\text{]}\cdot\text{[}15+2\sqrt{6}\text{]}\)
c.\(\text{[}\frac{4}{3}\cdot\sqrt{3}+\sqrt{2}+\sqrt{3\frac{1}{3}}\text{]}\cdot\text{[}\sqrt{1,2}+\sqrt{2}-4\sqrt{\frac{1}{5}}\text{]}=4\)
d. \(\sqrt{\text{[}1-\sqrt{1989}\text{]}^2}\cdot\sqrt{1990+2\sqrt{1989}}=1988\)
e. \(\frac{a-\sqrt{ab}+b}{a\sqrt{a}+b\sqrt{b}}-\frac{1}{a-b}=\frac{\sqrt{a}-\sqrt{b}-1}{a-b}\)với \(a>0;b>0\)và \(a\ne b\)
giải hệ phương trình :
a) \(\hept{\begin{cases}x\cdot\left(1+y-x\right)=-2\cdot y^2-y\\x\cdot\left(\sqrt{2\cdot y}-2\right)=y\cdot\left(\sqrt{x-1}-2\right)\end{cases}}\)
b) \(\hept{\begin{cases}1+x\cdot y+\sqrt{x\cdot y}=x\\\frac{1}{x\cdot\sqrt{x}}+y\cdot\sqrt{y}=\frac{1}{\sqrt{x}}+3\cdot\sqrt{y}\end{cases}}\)
Làm hộ mk nhé mk tick cho :))))))))))
giải pt ( đặt ẩn phụ)
1. \(x^2+\sqrt{x+2012}=2012\)
2.\(4\cdot\sqrt{\frac{3x+1}{x-1}}+\sqrt{\frac{x-1}{3x+1}}=4\)
3. \(\left(x-3\right)\cdot\left(x+1\right)+4\cdot\left(x-3\right)\cdot\sqrt{\frac{x+1}{x-3}}+3=0\)
giải hệ phương trình: A, \(\frac{1}{x}+\frac{1}{y}=9\) và \(\left(\frac{1}{\sqrt[3]{x}}+\frac{1}{\sqrt[3]{y}}\right)\cdot\left(\frac{1}{\sqrt[3]{x}}+1\right)\cdot\left(\frac{1}{\sqrt[3]{y}}+1\right)=18\)
B,\(3x^2-y=0\) và \(\left(\sqrt{5x^3-4}+2\sqrt[3]{7x^2-1}\right)\cdot\frac{y+4}{3}=2\cdot\left(y+19\right)\)
M=\(\frac{1+ab}{a+b}-\frac{1-ab}{a-b}\)
với a=\(\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
b=\(\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
Tính M