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a ) x = − 91 60 . b ) x = − 8 9 . c ) x = 35 19 . d ) x = 3 7 .
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<=> 75x+23 = 3x-1 or 75x+23 = -(3x-1)
<=> x = -1/3 or x = -11/39
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(x-2)(2y+3)=26=1.26=26.1=13.2=2.13
2y+3 luon le va >=3
(x-2)(2y+3)=2.13
2y+3=13=>y=5
x-2=2=>x=4
ds: x,y=(4,5)
Đáng ra đề bài phải bằng 26 chứ
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a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)
\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)
Vậy: \(1+2^2+2^3+...+2^{10}=2045\)
b)
a] \(60-3\left(x-1\right)=2^3\cdot3\)
\(\Rightarrow60-3\left(x-1\right)=24\)
\(\Rightarrow3\left(x-1\right)=36\)
\(\Rightarrow x-1=12\)
\(\Rightarrow x=13\)
b] \(\left(3x-2\right)^3=2\cdot2^5\)
\(\Rightarrow\left(3x-2\right)^3=2^6\)
\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)
\(\Rightarrow3x-2=2^2\)
\(\Rightarrow3x=6\)
\(x=2\)
c] \(5^{x+1}-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x\cdot4=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
d] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
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\(\frac{27}{23}+\frac{-4}{23}+\frac{1}{2}+\frac{-4}{8}< x< \frac{7}{3}+\frac{13}{41}+\frac{28}{41}\)
\(\Rightarrow\frac{27}{23}-\frac{4}{23}+\frac{1}{2}-\frac{4}{8}< x< \frac{7}{3}+\frac{13}{41}+\frac{28}{41}\)
\(\Rightarrow1+0< x< \frac{7}{3}+\frac{3}{3}\)
\(\Rightarrow1< x< \frac{10}{3}\)
\(\Rightarrow1< x< 3,333333333\)
\(\Rightarrow x\in\left\{2;3\right\}\)
Vậy : ....
ta co : \(\frac{27}{23}+\frac{-4}{23}+\frac{1}{2}+\frac{-4}{8}< x< \frac{7}{3}+\frac{13}{41}+\frac{28}{41}\)
=> \(1< x< \frac{10}{3}\)
vi x la so nguyen => \(1< x\le3\)
con lai ban tu lam
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=>(4-x:2)^3=1+2*(8-5)+1
=>(4-x:2)^3=2+2*3=8
=>4-x:2=2
=>x:2=2
=>x=4
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a) ( 1 + 3 + 5 + ....+ 97 + 99 ) - 2 x X = 500
Áp dụng công thức tính dãy số ta có :
\(1+3+5+...+99=\frac{\left[\left(99-1\right):2+1\right].\left(99+1\right)}{2}=50.100:2=50.50=2500\)
=> 2500 - 2X = 500
=> 2X = 2500 - 500 = 2000
=> X = 2000 : 2 = 1000
a) Ta có : 1 + 3 + 5 + ..... + 97 + 99
Số số hạng trên là :
( 99 - 1 ) : 2 + 1 = 50 số hạng :
Tổng trên là :
( 99 - 1 ) x 50 : 2 = 2450
Thế vào câu a ta được :
2450 - 2x = 500
=> 2x = 1950
=> x = 975
Kết quả 1: Rút gọn biểu thức
23 : x + 1
x2 + 23/x