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\(\frac{2}{1^2}.\frac{6}{2^2}.\frac{12}{3^2}.\frac{20}{4^2}...\frac{110}{10^2}.x=-20\)
\(\Leftrightarrow\frac{1.2}{1^2}.\frac{2.3}{2^2}.\frac{3.4}{3^2}.\frac{4.5}{4^2}...\frac{10.11}{10^2}.x=-20\)
\(\Leftrightarrow\frac{2}{1}.\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{11}{10}.x=-20\)
\(\Leftrightarrow11.x=-20\)
\(\Leftrightarrow x=\frac{-20}{11}\)
1) x - 36 + 12 = - x+ 10
=> x + x = 10 + 24
=> 2x = 34
=> x = 34/2 = 17
2) (x + 15) - (11 - x) = (-2)2
=> x + 15 - 11 + x = 4
=> 2x = 4 - 4
=> 2x = 0
=> x = 0
3) 40 - 4x2 = (-6)2
=> 40 - 4x2 = 36
=> 4x2 = 40 - 36
=> 4x2 = 4
=> x2 = 1
=> x = \(\pm\)1
4) (-50) + 10x2 = (-25) x |-2|
=> -50 + 10x2 = -50
=> 10x2 = -50 + 50
=> 10x2 = 0
=> x2 = 0
=> x = 0
5) |x + 1| = 2020
=> \(\orbr{\begin{cases}x+1=2020\\x+1=-2020\end{cases}}\)
=> \(\orbr{\begin{cases}x=2019\\x=-2021\end{cases}}\)
6) (x + 1)5 + 8 = 0 (xem lại đề)
7) (-20) + x3 : 16 = -24
=> x3 : 16 = -24 + 20
=> x3 : 16 = -4
=> x3 = -4 . 16
=> x3 = -64 = (-4)3
=> x = -4
9) x14 = x17
=> x14 - x17 = 0
=> x14(1 - x3) = 0
=> \(\orbr{\begin{cases}x^{14}=0\\1-x^3=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
10) (-36) + (1 - x)2 = 0
=> (1 - x)2 = 36
=> (1 - x)2 = 62
=> \(\orbr{\begin{cases}1-x=6\\1-x=-6\end{cases}}\)
=> \(\orbr{\begin{cases}x=-5\\x=7\end{cases}}\)
a,2A=8+23+24+25+............+221
2A-A=(8+23+24+25+...........+221)-(4+22+23+24+.............+220)
A=(8+23+221)-(4+22)
A=8+8+221-4-4
A=4+4+221
A=23+221
b,(x+1)+(x+2)+.............+(x+100)=5750
=>x+1+x+2+...........+x+100=5750
=>100x+(1+2+............+100)=5750
=>100x+\(\frac{100.\left(100+1\right)}{2}\)=5750
=>100x+5050=5750
=>100x=5750-5050
=>100x=700
=>x=700:100
=>x=7
2 mũ 2+2 mũ 3+2=20
\(2^x+2^{x+2}=20\Leftrightarrow2^x+2^x.2^2=20\)
\(\Leftrightarrow2^x\left(1+2^2\right)=20\Leftrightarrow2^x.5=20\Leftrightarrow2^x=4\Rightarrow x=2\)