Tính :
a) \(5\dfrac{1}{3}+2,5.\left(\dfrac{1}{3}-\dfrac{5}{12}\right)\)
b) \(\sqrt{12^2-44}-\left(1\dfrac{3}{4}-2\right)^2+\left(-1.5\right)^5:\left(\dfrac{-3}{2}\right)^4\)
Chứng minh rằng: \(\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+....+\dfrac{1}{\sqrt{100}}>10\)
1) Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{2010}=\dfrac{2010}{a}\)và a + b + c \(\ne\) \(-2010\). Tính a,b,c
2) Cho 3 tỉ số \(\dfrac{a}{b+c};\dfrac{b}{c+a};\dfrac{c}{a+b}\). Tính giá trị mỗi tỉ số.
3) Tìm GTNN của:
a) A = \(\sqrt{x+24}+\dfrac{4}{7}\)
b) B = \(\sqrt{2x+\dfrac{4}{13}}-\dfrac{13}{191}\)
4) Tìm GTLN của:
a) A = \(-\sqrt{x+\dfrac{5}{41}}+\dfrac{7}{12}\)
b) B = \(\dfrac{-5}{13}-\sqrt{x-\dfrac{2}{3}}\)
5) Tìm n, biết:
\(\sqrt{1+2+3+...+\left(n-1\right)+n+\left(n-1\right)+...+3+2+1=2010}\)
thực hiện phép tính
a. \(\dfrac{11}{21}+\dfrac{-2}{7}+\dfrac{10}{21}+\left(-1\dfrac{1}{5}\right)+\dfrac{-5}{7}\)
\(b.\left(0.25\right)^5.\left(-5\dfrac{5}{9}\right).\left(-4\right)^5\)
\(c.\dfrac{3}{22}.19\dfrac{1}{7}+\dfrac{3}{22}.2\dfrac{6}{7}-\sqrt{36}\)
Tính
\(\dfrac{3}{2}-\dfrac{5}{6}:\left(\dfrac{1}{2}\right)^2\) +\(\sqrt{4}\)
tìm x biết
a)\(\left(\dfrac{x}{2}-\dfrac{1}{3}\right)^2=\sqrt{16}\)
b)\(\dfrac{x+4}{2010}+\dfrac{x+3}{2011}=\dfrac{x+2}{2012}+\dfrac{x+1}{2013}\)
c)\(3^{x+2}+4\times3^{x+1}=7\times3^6\)
Bài 1 : thực hiện phép tính ( tính nhanh nếu có thể )
\(a.\dfrac{11}{17}-\dfrac{5}{13}+\dfrac{6}{17}+\dfrac{11}{25}-\dfrac{8}{13}\)
\(b.\sqrt{36}.\sqrt{0.25}+\sqrt{121}\)
\(c.\left(0.25\right)^3.4^8.\left(0.25\right)^5\)
\(d.\left(-6,5\right).2,8+2,8.\left(-3,5\right)\)
\(\sqrt{1,69}.\left(2\sqrt{x}+\sqrt{\dfrac{81}{121}}\right)=\dfrac{13}{10}\left(x>0\right)\)
GIÚP MIK VỚI
Rút gọn:
\(A=\left[\left(\dfrac{3}{1+x}-\dfrac{x}{x^2+x+1}\right):\dfrac{2x^2+3x}{x+1}+\dfrac{3}{x+1}\right]\cdot\dfrac{x^2+x}{1+3x}\)
\(B=\left[\dfrac{a}{2a-6}-\dfrac{a^2}{a^2-9}+\dfrac{a}{2a-9}\cdot\left(\dfrac{3}{a}+\dfrac{1}{3-a}\right)\right]:\dfrac{a^2-5a-6}{18-2a^2}\)