( 1/24 x 25 + 1/25 x 26 + ... + 1/29 x 30 ) x 150 + 103/100 [ 103/100 x ( X - 1 ) ] = 22
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x + 20 + 21 + x + 22 + 23 + x + 24 + 25 + x + 26 + 27 + x + 28 + 29 + x + 30 = 330
6x + (30 + 20) . (30 - 20 + 1) : 2 = 330
6x + 50 . 11 : 2 = 330
6x + 275 = 330
6x = 330 - 275
6x = 55
x = 55 : 6
x = 55/6
\(x+20+21+x+22+23+x+24+25+x+26+27+x+28+29+x+30=330\)
\(\Rightarrow\left(x+x+x+x+x+x\right)+\left(20+21+22+23+24+25+26+27+28+29+30\right)=330\)
\(\Rightarrow6x+\left[\left(30-20\right):1+1\right]\left(20+30\right):2=330\)
\(\Rightarrow6x+11.50:2=330\)
\(\Rightarrow6x+275=330\)
\(\Rightarrow6x=55\)
\(\Rightarrow x=\dfrac{55}{6}\)
x + 20 + 21 + x + 22 + 23 + x + 24 + 25 + x + 26 + 27 + x + 28 + 29 + x + 30 = 330
6x + (30 + 20) . (30 - 20 + 1) : 2 = 330
6x + 50 . 11 : 2 = 330
6x + 275 = 330
6x = 330 - 275
6x = 55
x = 55 : 6
x = 55/6
a) x . 3/5 = 2/3
<=> x = 2/3 : 3/5
<=> x = 2/3 . 5/3
<=> x = 10/9
Học tốt nha! :)
Bài 1:
a) dễ, tự làm :)))
b) \(B=2^{100}-2^{99}-2^{98}-...-2^2-2^1-1.\)
\(\Rightarrow B=2^{100}-\left(2^{99}+2^{98}+2^{97}+...+2^2+2^1+1\right).\)
Đặt: \(M=2^{99}+2^{98}+2^{97}+...+2^2+2^1+1.\)
\(\Rightarrow2M=2\left(2^{99}+2^{98}+2^{97}+...+2^2+2^1+1\right).\)
\(\Rightarrow2M=2^{100}+2^{99}+2^{98}+...+2^3+2^2+2^1.\)
\(\Rightarrow2M-M=\left(2^{100}+2^{99}+2^{98}+...+2^3+2^2+2^1\right)-\left(2^{99}+2^{98}+2^{97}+...+2^2+2^1+1\right).\)
\(\Rightarrow M=2^{100}-1.\)
Ta có: \(B=2^{100}-\left(2^{99}+2^{98}+2^{97}+...+2^2-2^1-2\right).\)
\(\Rightarrow B=2^{100}-\left(2^{100}-1\right).\)
\(\Rightarrow B=\left(2^{100}-2^{100}\right)+1.\)
\(\Rightarrow B=1.\)
Vậy..........
Bài 2:
a) \(\left(x-1\right)\left(x-5\right)< 0.\)
\(\Rightarrow x-1\) và \(x-5\) trái dấu.
mà \(x-1>x-5.\)
\(\Rightarrow\left[{}\begin{matrix}x-1>0.\\x-5< 0.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>1.\\x< 5.\end{matrix}\right.\Leftrightarrow1< x< 5.\)
mà \(x\in Z.\)
\(\Rightarrow x\in\left\{2;3;4\right\}.\)
Vậy..........
b) \(\left(x^2-25\right)\left(x^2-5\right)< 0.\)
\(\Rightarrow x^2-25\) và \(x^2-5\) trái dấu.
mà \(x^2-25< x^2-5.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-25< 0.\\x^2-5>0.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2< 25.\\x^2>5.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x< 5.\\x>\sqrt{5}\left(loại\right).\end{matrix}\right.\Rightarrow x< 5.\)
Vậy..........