(-1 1/2)2 + 1,2
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2A = 1 + \(\dfrac{1}{2}\)+\(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+...+\(\dfrac{1}{2^{99}}\)
2A - A= 1- \(\dfrac{1}{2^{100}}\)
A= 1
Giải bài toán sau 1 + 1/2 + 1/2 mũ 2 + 1,2 mũ 3 + 1,2 mũ 4 + 3 chấm ba chấm + 1,2 mũ 99 + 1/2 mũ 100
Gọi biểu thức trên là Acó:
A=1+1/2+1/2^2+1/2^3+...+1/2^99+1/2^100
2A=1/2+1/2^2+1/2^3+....+1/2^99+1/2^100+1/2^101
2A-A=(1/2+1/2^2+1/2^3+....+1/2^99+1/2^100+1/2^101)-(1+1/2+1/2^2+1/2^3+...+1/2^99+1/2^100)
A=1/2^101-1
A=-1
a) \(2^x=8\)
⇔ \(2^x=2^3\)
⇒ \(x=3\)
b) \(3^x=27\)
⇔ \(3^x=3^3\)
⇒ \(x=3\)
c) \(\left(-\dfrac{1}{2}\right)x=\left(-\dfrac{1}{2}\right)^4\)
⇔ \(x=\left(-\dfrac{1}{2}\right)^4\div\left(-\dfrac{1}{2}\right)\)
⇔ \(x=\left(-\dfrac{1}{2}\right)^3\)
d) \(x\div\left(-\dfrac{3}{4}\right)=\left(-\dfrac{3}{4}\right)^2\)
⇔ \(x=\left(-\dfrac{3}{4}\right)^2\cdot\left(-\dfrac{3}{4}\right)\)
⇔ \(x=\left(-\dfrac{3}{4}\right)^3=-\dfrac{27}{64}\)
d) \(\left(x+1\right)^3=-125\)
⇔ \(\left(x+1\right)^3=\left(-5\right)^3\)
⇔ \(x+1=-5\)
⇔ \(x=-5-1=-6\)
2:
a: (x-1,2)^2=4
=>x-1,2=2 hoặc x-1,2=-2
=>x=3,2(loại) hoặc x=-0,8(loại)
b: (x-1,5)^2=9
=>x-1,5=3 hoặc x-1,5=-3
=>x=-1,5(loại) hoặc x=4,5(loại)
c: (x-2)^3=64
=>(x-2)^3=4^3
=>x-2=4
=>x=6(nhận)
`1/2+2 1/4x-2/3=(3/2:5/4-1/2)`
`=>9/4x-1/6=6/5-6/5=0`
`=>9/4x=1/6`
`=>x=2/27`
Vậy...
tính
1)\(\left(\dfrac{1}{2}\right)^2\)
\(=\dfrac{1}{2}\times\dfrac{1}{2}\)
\(=\dfrac{1}{4}\)
2)\(3,6^2\div1,2^2\)
\(=\left(\dfrac{18}{5}\right)^2\div\left(\dfrac{6}{5}\right)^2\)
\(=\left(\dfrac{18}{5}\times\dfrac{18}{5}\right)\div\left(\dfrac{6}{5}\times\dfrac{6}{5}\right)\)
\(=\dfrac{324}{25}\div\dfrac{36}{25}\)
\(=\dfrac{324}{25}\times\dfrac{25}{36}\)
\(=\dfrac{8100}{900}\)
\(=9\)
\(=\left[\dfrac{1}{4}-\dfrac{6}{5}\right]-\dfrac{4}{5}+\dfrac{3}{4}\)
\(=\dfrac{1}{4}-\dfrac{6}{5}-\dfrac{4}{5}+\dfrac{3}{4}\)
=1/4+3/4-6/5-4/5
=1-2
=-1
\(x\cdot\frac{1}{1\cdot2}+x\cdot\frac{1}{2\cdot3}+x\cdot\frac{1}{3\cdot4}+...+x\cdot\frac{1}{9\cdot10}=2\)
\(\Leftrightarrow x\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\right)=2\)
\(\Leftrightarrow x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)=2\)
\(\Leftrightarrow x\cdot\left(1-\frac{1}{10}\right)=2\)
\(\Leftrightarrow x\cdot\frac{9}{10}=2\)
\(\Leftrightarrow x=2\cdot\frac{10}{9}=\frac{20}{9}\)
\(\left(-1\frac{1}{2}\right)^2+1,2\)
=\(\left(\frac{-3}{2}\right)^2+\frac{6}{5}\)
=\(\frac{9}{4}+\frac{6}{5}\)
=\(\frac{45}{20}+\frac{24}{20}\)
=\(\frac{69}{20}\)