1) ( 2x -15 )5 = ( 2x - 15 )3
( 2x -15 )5 - ( 2x - 15 )3 = 0
( 2x - 15 )3 . [ ( 2x - 15 )2 - 1 ] = 0
\(\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)
\(\orbr{\begin{cases}2x-15=0\\2x-15=1\end{cases}}\)
\(\orbr{\begin{cases}2x=15\\2x=16\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{15}{2}\\x=8\end{cases}}\)
Tìm x:
1) \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
2) \(\left(19x+2\cdot5^2\right):14=\left(13-8\right)^2-4^2\)
1. Tìm x
a) \(2^x+5=21\)
b) \(2^x-1+3^2=5^2+2\cdot5\)
c) \(\left(2x-1\right)^3+5=130\)
d) \(5^{2x-3}-2\cdot5^2=5^2\)
e) \(3^{2x+1}-2=3^2+\left[5^2-3\left(2^2-1\right)\right]\)
f) \(\left(7^x-11\right)^3=2^5\cdot5^2+200\)
g) \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
Rút gọn:
a,\(A=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
b,\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{2014\cdot2016}\right)\)
\(\dfrac{99}{100}:\left(\dfrac{1}{4}-\dfrac{1}{12}+\dfrac{1}{3}\right)-\left(\dfrac{-7}{5}\right)^2\)
\(\dfrac{13}{15}\cdot0,25\cdot3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\)
Bài 2 : Tìm x , biết :
a, \(\left(19x+2\cdot5^2\right)\text{ : }14=\left(13-8\right)^2-4^2\)
b, \(x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+30\right)=1240\)
c, \(11-\left(-53+x\right)=97\)
d, \(-\left(x+84\right)+213=-16\)
e, \(13-12+11+10-9+8-7-6+5-4+3+2-1=x\)
trình bày cách tính nhanh các phép tính sau đây
a)\(\frac{2^8\cdot6}{3^3\cdot5^4}:\frac{8^3\cdot9}{5^3\cdot3^3}-\left(2^{14}+3^{19}\right)\cdot\left(3^{81}+5^{64}\right)\left(2^4-4^2\right)\)
Tính tổng :
a) \(A=\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot14}+\frac{1}{14\cdot15}+\frac{13}{15\cdot28}\)
b) \(B=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
c) \(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
d) \(D=\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)\left(n+3\right)}\)
e) \(E=\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{37\cdot38\cdot39}\right)\cdot1482\cdot185\cdot8\)
Tìm x:
\(\frac{\left(13\frac{2}{9}-15\frac{2}{3}\right)\cdot\left(30^2-5^4\right)}{\left(18\frac{3}{7}-17\frac{1}{4}\right)\cdot\left(25-12\cdot5^2\right)}\cdot x=\frac{\frac{2}{11}+\frac{3}{13}+\frac{4}{15}+\frac{5}{17}}{4\frac{1}{11}+\frac{5}{13}+\frac{9}{15}+\frac{13}{17}}\)
a) \(\dfrac{1}{2}\cdot\dfrac{-3}{4}\cdot\dfrac{-5}{8}\cdot\dfrac{-8}{9}\)
b) \(\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}\right)\cdot\left(\dfrac{10\cdot13}{3}-\dfrac{2^2}{3}-\dfrac{5^3}{3}\right)\)
câu này làm cx đc hoặc ko làm cx ko sao :)
\(\dfrac{8}{9}+\dfrac{1}{9}\cdot\dfrac{2}{9}+\dfrac{1}{9}\cdot\dfrac{7}{9}\)
