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LM
Lê Minh Vũ
VIP
7 tháng 8 2023
Bài 1:
a) \(\dfrac{9}{20}-\dfrac{8}{15}\times\dfrac{5}{12}\)
\(=\dfrac{9}{20}-\dfrac{2}{9}\)
\(=\dfrac{41}{180}\)
b) \(\dfrac{2}{3}\div\dfrac{4}{5}\div\dfrac{7}{12}\)
\(=\dfrac{2}{3}\times\dfrac{5}{4}\times\dfrac{12}{7}\)
\(=\dfrac{5}{6}\times\dfrac{12}{7}\)
\(=\dfrac{10}{7}\)
c) \(\dfrac{7}{9}\times\dfrac{1}{3}+\dfrac{7}{9}\times\dfrac{2}{3}\)
\(=\dfrac{7}{9}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)
\(=\dfrac{7}{9}\times1\)
\(=\dfrac{7}{9}\)
LM
Lê Minh Vũ
VIP
7 tháng 8 2023
Bài 2:
a) \(2\times\left(x-1\right)=4026\)
\(\left(x-1\right)=4026\div2\)
\(x-1=2013\)
\(x=2014\)
Vậy: \(x=2014\)
b) \(x\times3,7+6,3\times x=320\)
\(x\times\left(3,7+6,3\right)=320\)
\(x\times10=320\)
\(x=320\div10\)
\(x=32\)
Vậy: \(x=32\)
c) \(0,25\times3< 3< 1,02\)
\(\Leftrightarrow0,75< 3< 1,02\) ( S )
=> \(0,75< 1,02< 3\)
PT
1
10 tháng 8 2021
a: Ta có: \(20:\left(x+1\right)=\left(5^2+1\right):13\)
\(\Leftrightarrow x+1=10\)
hay x=9
b: Ta có: \(320:\left(x-1\right)=2^2\cdot5^2-20\)
\(\Leftrightarrow x-1=4\)
hay x=5
23 tháng 7 2018
a) (2x-2)3 = 27 = 33
=> 2x - 2 = 3
2x = 5
x = 5/2
b) (3x-1)2 = 64 = 82 = (-8)2
=>...
rùi bn lm như phần a nha
c) 5x+1 = 1/125 = 5-3 ( hình như bn chép sai đề)
=> x + 1 = -3
x = -4
d) 2x+1+2x+3 = 320
2x.2 +2x.23 = 320
2x.(2+8) = 320
2x.10 = 320
2x = 32 = 25
=> x = 5
8 tháng 7 2019
1 a, Ta có: \(36^5\): \(18^5\)= \(\left(36:18\right)^5\)= \(2^5\)= \(32\)
8 tháng 7 2019
\(1b.\)\(24\)\(5^3\)+ \(5^2\). \(5^3\)= \(5^2\). \(\left(5^3+24\right)\)= \(25.149\)= \(3725\)
H9
HT.Phong (9A5)
CTVHS
9 tháng 1
a) \(\dfrac{2x+5}{2x+1}=\dfrac{2x+1+4}{2x+1}=\dfrac{2x+1}{2x+1}+\dfrac{4}{2x+1}=1+\dfrac{4}{2x+1}\)
Để \(\dfrac{2x+5}{2x+1}\in Z\) thì \(\dfrac{4}{2x+1}\in Z\)
\(\Rightarrow4\) ⋮ \(2x+1\)
\(\Rightarrow2x+1\inƯ\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)
\(\Rightarrow2x\in\left\{0;-2;1;-3;3;-5\right\}\)
\(\Rightarrow x\in\left\{0;-1;\dfrac{1}{2};-\dfrac{3}{2};\dfrac{3}{2};-\dfrac{5}{2}\right\}\)
Mà x nguyên \(\Rightarrow\text{x}\in\left\{0;-1\right\}\)
b) \(\dfrac{3x+5}{x+1}=\dfrac{3x+3+2}{x+1}=\dfrac{3\left(x+1\right)+2}{x+1}=\dfrac{3\left(x+1\right)}{x+1}+\dfrac{2}{x+1}=3+\dfrac{2}{x+1}\)
Để \(\dfrac{3x+5}{x+1}\in Z\) thì \(\dfrac{2}{x+1}\in Z\)
\(\Rightarrow2\) ⋮ \(x+1\)
\(\Rightarrow x+1\inƯ\left(2\right)=\left\{1;-1;2;-2\right\}\)
\(\Rightarrow x\in\left\{0;-2;1;-3\right\}\)
c) \(\dfrac{3x+8}{x-1}=\dfrac{3x-3+11}{x-1}=\dfrac{3\left(x-1\right)+11}{x-1}=\dfrac{3\left(x-1\right)}{x-1}+\dfrac{11}{x-1}=3+\dfrac{11}{x-1}\)
Để: \(\dfrac{3x+8}{x-1}\in Z\) thì \(\dfrac{11}{x-1}\in Z\)
\(\Rightarrow11\) ⋮ \(x-1\)
\(\Rightarrow x-1\inƯ\left(11\right)=\left\{1;-1;11;-11\right\}\)
\(\Rightarrow x\in\left\{2;0;12;-10\right\}\)
d) \(\dfrac{5x+12}{x-2}=\dfrac{5x-10+22}{x-2}=\dfrac{5\left(x-2\right)+22}{x-2}=\dfrac{5\left(x-2\right)}{x-2}+\dfrac{22}{x-2}=5+\dfrac{22}{x-2}\)
Để: \(\dfrac{5x+12}{x-2}\in Z\) thì \(\dfrac{22}{x-2}\in Z\)
\(\Rightarrow22\) ⋮ \(x-2\)
\(\Rightarrow x-2\inƯ\left(22\right)=\left\{1;-1;2;-2;11;-11;22;-22\right\}\)
\(\Rightarrow x\in\left\{3;1;4;0;13;-9;24;-20\right\}\)
e) \(\dfrac{7x-12}{x+16}=\dfrac{7x+112-124}{x+16}=\dfrac{7\left(x+16\right)-124}{x+16}=\dfrac{7\left(x+16\right)}{x+16}-\dfrac{124}{x+16}=7-\dfrac{124}{x+16}\)
Để \(\dfrac{7x-12}{x+16}\in Z\) thì \(\dfrac{124}{x+16}\in Z\)
\(\Rightarrow124\) ⋮ \(x+16\)
\(\Rightarrow x+16\inƯ\left(124\right)=\left\{1;-1;2;-2;4;-4;31;-31;62;-62;124;-124\right\}\)
\(\Rightarrow x\in\left\{-15;-17;-14;-18;-12;-20;15;-47;46;-78;108;-140\right\}\)
DN
23 tháng 12 2021
\(3^x+3^{x+1}=3^8.2+2.3^8.2017^0\)
\(3^x+3^x.3=3^8.2^2\)
\(3^x=3^8.2^2:3\)
\(3^x=3^7.2^2\)
23 tháng 12 2021
3x+3x+1=38.2+2.38.201703x+3x+1=38.2+2.38.20170
3x+3x.3=38.223x+3x.3=38.22
3x=38.22:33x=38.22:3
3x=37.223x=37.22
DH
1
17 tháng 12 2021
b: \(\Leftrightarrow x+8\in\left\{1;-1;5;-5\right\}\)
hay \(x\in\left\{-7;-9;-3;-13\right\}\)
\(8^{x+1}+2^{3x+1}=320\)
\(\left(2^3\right)^{\left(x+1\right)}+2^{3x}.2=320\)
\(2^{3x}.2^3+2^{3x}.2=320\)
\(2^{3x}\left(8+2\right)=320\)
\(2^{3x}=32\)
\(2^{3x}=2^5\)
\(3x=5\)
\(x=\frac{5}{3}\)