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a, 3 : ( 1 - 3/2x ) = 4 : ( 2 - x )
<=> \(\frac{3}{1-\frac{3}{2}x}=\frac{4}{2-x}\)
<=> 3 ( 2 - x ) = 4 ( 1 - 3/2x )
<=> 6 - 3x = 4 - 6x
<=> -3x + 6x = 4 - 6
<=> 3x = -2
<=> x = -2/3
b, 2.3x + 3x-1 = 7( 32 + 2.62 )
b, 2.3x + 3x-1 = 7( 32 + 2.62 )
<=> 2.3x + 3x-1 = 7.81
<=> 3x-1(2.3 + 1) = 7.81
<=> 3x-1.7 = 7.81
<=> 3x-1=81
<=> 3x-1 = 34
=> x - 1 = 4 => x = 5
Áp dụng công thức: (n-2)n(n+2) = n3 - 4n => n3 = (n-2).n.(n+2) + 4n
b18) Áp dụng: ta có: 23 = 4.2; 43 = 2.4.6 + 4.4 ; 63 = 4.6.8 + 4.6; ...; 1003 = 98.100.102 + 4.100
=> A = 4.2 + 2.4.6 + 4.4 + 4.6.8 + 4.6 +...+ 98.100.102 + 4.100
= (2.4.6 + 4.6.8 + 6.8.10 +....+ 98.100.102 ) + 4.(2 + 4 + 6 + ...+ 100) = B + 4.C
Tính B = 2.4.6 + 4.6.8 + 6.8.10 +....+ 98.100.102
=> 8.B = 2.4.6.8 + 4.6.8.8 + 6.8.10.8 +...+ 98.100.102.8
= 2.4.6.8 + 4.6.8 (10 - 2) + 6.8.10.(12 - 4) +...+ 98.100.102.(104 - 96)
= 2.4.6.8 + 4.6.8.10 - 2.4.6.8 + 6.8.10.12 - 4.6.8.10 +...+ 98.100.102.104 - 96.98.100.102
= (2.4.6.8 + 4.6.8.10 + 6.8.10.12 +...+ 98.100.102.104) - (2.4.6.8 + 4.6.8.10 +...+ 96.98.100.102)
= 98.100.102.104
=> B =98.100.102.104 : 8 = 12 994 800
C = 2+ 4+ 6 +..+100 = (2+100) . 50 : 2 = 2550
Vậy A = B +4C = 12 994 800 + 4. 2550 = 13 005 000
\(\left(2x-3\right)^2=25\)
\(\Rightarrow\left(2x-3\right)^2=5^2\)
\(\Rightarrow2x-3=5\)
\(\Rightarrow2x=5+3\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=4\)
Bài 1
A = \(\frac{3}{7}.\left(\frac{3}{7}\right)^{19}\)= \(\left(\frac{3}{7}\right)^{20}\)
B = \(\left[\left(-\frac{3}{7}\right)^5\right]^4\)= \(\left(-\frac{3}{7}\right)^{20}\)
Bài 2
a. (2x - 3)2 = 25
<=> \(\orbr{\begin{cases}2x-3=5\\2x-3=-5\end{cases}}\)
<=> \(\orbr{\begin{cases}x=4\\x=-1\end{cases}}\)
Vậy ...
b. \(\frac{27}{3^x}\)= 3
<=> 27 = 31+x
<=> 33 = 31+x
<=> 3 = 1 + x
<=> x = 2
Bài 1
\(A=\frac{3}{7}\cdot\left(\frac{3}{7}\right)^{19}=\left(\frac{3}{7}\right)^{18}\)
\(B=\left[\left(-\frac{3}{7}\right)^5\right]^4=\left(-\frac{3}{7}\right)^{20}=\left(\frac{3}{7}\right)^{20}\)
=> A<B
Bài 2
a
\(\left(2x-3\right)^2=25\)
\(\Rightarrow\orbr{\begin{cases}2x-3=5\\2x-3=-5\end{cases}}\)
\(\Rightarrow x=4;x=-1\)
b
\(\frac{27}{3^x}=3\)
\(\Leftrightarrow27=3^{x+1}\)
\(\Leftrightarrow3^{x+1}=3^3\)
\(\Rightarrow x=2\)
Bài 1 :
\(A=\frac{3}{7}\cdot\left(\frac{3}{7}\right)^{19}\)
\(A=\left(\frac{3}{7}\right)^{20}\)
\(B=\left[\left(-\frac{3}{7}\right)^5\right]^4\)
\(B=\left(-\frac{3}{7}\right)^{20}\)
\(B=\left(\frac{3}{7}\right)^{20}\)
-_^
Nhầm ! Bài 1 quên kết luận ^^
\(\Rightarrow\text{ }A=B\)
Bài 2 : Tìm x \(\in\)Z :
\(\left(2x-3\right)^2=25\)
\(\left(2x-3\right)^2=\left(\pm5\right)^2\)
\(2x-3=\pm5\)
\(\Rightarrow\orbr{\begin{cases}2x-3=-5\\2x-3=5\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}2x=-5+3=-2\\2x=5+3=8\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=-2\text{ : }2=-1\\x=8\text{ : }2=4\end{cases}}\)
\(\Rightarrow\text{ }x\in\left\{-1\text{ ; }4\right\}\)
\(\frac{27}{3^x}=3\)
\(\frac{3^3}{3^x}=3\)
\(\Leftrightarrow\text{ }3^3=3^x\cdot3\)
\(3^3=3^{x+1}\)
\(\Rightarrow\text{ }x+1=3\)
\(x=3-2\)
\(x=2\)