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Đặt A = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64
2A = 1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32
2A + A = (1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32) + (1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64)
3A = 1- 1/64 = 63/64 => A = 63/64 : 3 = 21/64
Dễ thấy: 1/3 = 21/63 > 21/64
Vậy A < 1/3 (ĐPCM)
a) \(x-2=-6\)
\(x=-6+2\)
\(x=-4\)
b) \(15-\left(x-7\right)=-21\)
\(x-7=36\)
\(x=43\)
c) \(4.\left(3x-4\right)-2=18\)
\(4\left(3x-4\right)=20\)
\(3x-4=5\)
\(3x=9\)
\(x=3\)
d) \(\left(3x-6\right)+3=32\)
\(3x-6=29\)
\(3x=29+6\)
\(3x=35\)
\(x=\frac{35}{3}\)
e) \(\left(3x-6\right).3=32\)
\(3x-6=\frac{32}{3}\)
\(3x=\frac{32}{3}+6\)
\(3x=\frac{50}{3}\)
\(x=\frac{50}{9}\)
f) \(\left(3x-6\right):3=32\)
\(3x-6=96\)
\(3x=102\)
\(x=34\)
g) \(\left(3x-6\right)-3=32\)
\(3x-6=35\)
\(3x=41\)
\(x=\frac{41}{3}\)
h) \(\left(3x-2^4\right).7^3=2.7^4\)
\(\left(3x-2^4\right)=2.7=14\)
\(\left(3x-16\right)=14\)
\(3x=14+16=30\)
\(x=10\)
i) \(\left|x\right|=\left|-7\right|\)
\(\left|x\right|=7\)
\(\Rightarrow\orbr{\begin{cases}x=7\\x=-7\end{cases}}\)
k) \(\left|x+1\right|=2\)
\(\Rightarrow\orbr{\begin{cases}x+1=2\\x+1=-2\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=-3\end{cases}}}\)
l) \(\left|x-2\right|=3\)
\(\Rightarrow\orbr{\begin{cases}x-2=3\\x-2=-3\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=-1\end{cases}}}\)
m) \(x+\left|-2\right|=0\)
\(x+2=0\)
\(x=-2\)
o) \(72-3\left|x+1\right|=9\)
\(3\left|x-1\right|=63\)
\(\left|x-1\right|=21\)
\(\Rightarrow\orbr{\begin{cases}x-1=21\\x-1=-21\end{cases}\Rightarrow\orbr{\begin{cases}x=22\\x=-20\end{cases}}}\)
p) Ta có: \(\left|x-1\right|=3\)
\(\Rightarrow\orbr{\begin{cases}x-1=3\\x-1=-3\end{cases}}\)
mà \(x+1< 0\)
\(\Rightarrow x-1=-3\)
\(\Rightarrow x=-2\)
q) \(\left(x-2\right)\left(x+4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-2=0\\x+4=0\end{cases}\Rightarrow\orbr{\begin{cases}x=2\\x=-4\end{cases}}}\)
hok tốt!!
a: \(A=\left|2x-1\right|+2019>=2019\)
Dấu '=' xảy ra khi x=1/2
b: \(=-3\left|7x-4\right|+2< =2\)
Dấu '=' xảy ra khi x=4/7
c: \(=2\left(x-1\right)^2+\left|3y+1\right|-2018>=-2018\)
Dấu '=' xảy ra khi x=1 và y=-1/3
b)
\(\dfrac{1}{2}\left(\dfrac{4}{5}-\dfrac{3}{2}\right)+x=5\left(x-\dfrac{1}{3}\right)\)
=> \(-\dfrac{7}{20}+x=5x-\dfrac{5}{3}\)
=> \(\dfrac{79}{60}=4x\)
=> \(\dfrac{79}{240}=x\)
Vậy \(\dfrac{79}{240}=x\)
c)
\(2\left(x-5\right)-3\left(x+7\right)=14\)
=> \(2x-10-3x-21=14\)
=> \(-x-31=14\)
=> \(-x=45\)
=> x = -45
Vậy x là -45