Vì 2 + 3 +.. +9 + 1 + 2 + 3 + 4 = 200( 1 + 2 +3 +.. +9) - 199 ( 1 + 2 + 3 +.. +9) + 9 ( chuyển vế)
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 9 ( vì2+ 3 +4 = 9 ) = 1 + 2 + 3 +.. +9 + 9
Tìm x liên quan đến lũy thừa:
1, \(\left(3x-\dfrac{1}{5}\right)^2=\left(\dfrac{-3}{25}\right)^2\)
2, \(\left(2x-\dfrac{1}{3}\right)^2=\left(\dfrac{-2}{9}\right)^2\)
3, \(\left(\dfrac{1}{3}-x\right)^2=\dfrac{9}{25}\)
4, \(\left(5-x\right)^2=25\)
Tối giản phân số sau bằng cách thuận tiện:
\(\frac{\left(2^4+2^2+1\right)\left(4^4+4^2+1\right)\left(6^4+6^2+1\right)\left(8^4+8^2+1\right)\left(10^4+10^2+1\right)}{\left(3^4+3^2+1\right)\left(5^4+5^2+1\right)\left(7^4+7^2+1\right)\left(9^4+9^2+1\right)\left(11^4+11^2+1\right)}\)
Tính giá trị của biểu thức:
\(A=\dfrac{-3}{7}.\dfrac{5}{9}+\dfrac{4}{9}.\dfrac{-3}{7}+\left(-2022\right)^0\)
\(B=0,75-\left(2\dfrac{1}{3}+0,75\right)+3^2.\left(-\dfrac{1}{9}\right)\)
\(C=2\dfrac{6}{7}.\left[\left(\dfrac{-7}{5}-\dfrac{3}{2}:\dfrac{-5}{-4}\right)+\left(\dfrac{3}{2}\right)^2\right]\)
\(D=\dfrac{2}{7}+\dfrac{5}{7}.\left(\dfrac{3}{5}-0,25\right).\left(-2\right)^2+35\%\)
\(E=1\dfrac{13}{15}.0,75-\left(\dfrac{11}{20}+25\%\right):1\dfrac{2}{5}\)
\(F=\dfrac{\dfrac{5}{3}-\dfrac{5}{7}+\dfrac{5}{9}}{\dfrac{10}{3}-\dfrac{10}{7}+\dfrac{10}{9}}\)
Tìm x:
a,\(x:\left(9\frac{1}{2}-\frac{3}{2}\right)=\frac{\frac{2}{5}+\frac{4}{9}-\frac{5}{11}}{\frac{8}{5}+\frac{16}{9}-\frac{20}{11}}\)
b,\(\left|2x-\frac{1}{3}\right|-\left(-2^2\right)=4\left(\frac{1}{-2}\right)^3\)
a\(\left[6+\left(\frac{1}{2}\right)^3-\left|-\frac{1}{2}\right|\right]:\frac{3}{12}\)
b\(\frac{4}{9}.19\frac{1}{3}-\frac{4}{9}.39\frac{1}{3}\)
c\(\left(-\frac{1}{2}\right)^2:\frac{1}{4}-2\left(-\frac{1}{2}\right)\)
Tìm số tự nhiên n, biết :
a/ \(\left(2.n-1\right)^4:\left(2.n-1\right)=27\)
b/ \(\left(2n+1\right)^5:\left(2.n+1\right)^2=1\)
c/ \(\left(n+1\right)^3:\left(n+1\right)=4\)
d/ \(\left(21+n\right):9=9^5:9^4\)
tính nhanh
a, \(\frac{-2}{5}\cdot\left(\frac{5}{17}-\frac{9}{15}\right)-\frac{2}{5}\cdot\frac{2}{17}+\frac{-2}{5}\)
b, \(\frac{1}{5}\cdot\left(\frac{4}{13}-\frac{9}{11}\right)+\frac{1}{3}\left(\frac{9}{13}-\frac{4}{22}\right)\)
c, \(\left(\frac{1}{2}+1\right)\cdot\left(\frac{1}{3}+1\right)\cdot\left(\frac{1}{4}+1\right)\cdot...\cdot\left(\frac{1}{99}+1\right)\)
d, \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)
\(A=-5^{22}-\left\{-222-\left[-122-\left(100-5^{22}\right)+2022\right]\right\}\)
\(B=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{20}\left(1+2+3+...+20\right)\)
\(C=\dfrac{5.4^6.9^4-3^9.\left(-8\right)^4}{4.2^{13}.3^8+2.8^4.\left(-27\right)^3}\)
1 tính
a \(\left(\frac{9}{14}-\frac{9}{21}\right):\left(\frac{4}{5}+\frac{5}{6}\right)\)
b \(\frac{7}{10}-\frac{-3}{4}+\frac{-5}{6}-\frac{1}{5}+\frac{-2}{3}\)
c \(\left(-2\right)^2.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)
d \(-\frac{1}{7}.\left(9\frac{1}{2}-0,75\right):\frac{2}{7}+0,625:1\frac{2}{3}\)
