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Giải :
a) x + ( x + 1 ) + ( x + 2 ) + ... + ( x + 50 ) = 2040
=> 51x + ( 1 + 2 + 3 + ... + 50 ) = 2040
=> 51x + ( 50 + 1 ) . 50 : 2 = 2040
=> 51x + 1275 = 2040
=> 51x = 765
=> x = 15
b) 1 + 2 + 3 + ... + x = 300
=> ( x + 1 ) . x : 2 = 300
=> ( x + 1 ) . x = 600
=> ( x + 1 ) . x = 25 . 24
=> x = 24
Bài 1 : 15 = 3.5; 35 = 5.7 ; 50 = 2.52
\(\Rightarrow\)ƯCLN (15, 35, 50) = 5
\(\Rightarrow\)BCNN = 2.3.52.7 = 1050
Bài 2 :
Ta có: 2.3.5 = 30
Vậy A = {300, 330, 360, 390} có 4 phần tử
1)
a) (a-b) - (c-b) - a= a - b - c + b - a = -c
b) -(300 - 400) + (300 - 400) + 100 = 100
2) a) 4x - 20 = 50 - ( 30 -3x)
4x - 20 = 50 - 30 + 3x
4x - 3x = 50 - 30 + 20= 40
x = 40
b) 100 - (-5x) = 40 - (-4x +10)
100 + 5x = 40 + 4x -10
5x - 4x = 40 - 10 -100
x = -70
c) (-50) + (-7x) = 100 - 8x
-7x + 8x = 100 + 50
x = 150
a)\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{21}{39}+\frac{49}{21}.\frac{8}{15}\)
=\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{7}{13}+\frac{7}{13}.\frac{8}{15}\)
=\(\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}-\frac{8}{15}\right)\)
=\(\frac{7}{13}.\frac{7}{12}\)
=\(\frac{49}{156}\)
b)\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
=\(a.\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
=a . 0
=0
Bài 2
a)Có
\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)
Vì 8<9 =>\(8^{100}< 9^{100}\) =>\(3^{200}>2^{300}\)
\(a,2^{700}=\left(2^7\right)^{100}=128^{100}\)
\(5^{300}=\left(5^3\right)^{100}=125^{100}\)
Có \(128^{100}>125^{100}\Rightarrow2^{700}>5^{300}\)
\(b,S=1+2+2^2+...+2^{50}\)
\(\Rightarrow2S=2+2^2+2^3+...+2^{51}\)
\(\Rightarrow2S-S=S=2^{51}-1< 2^{51}\)
a) Ta có :
\(2^{700}=\left(2^7\right)^{100}=128^{100}\)
\(5^{300}=\left(5^3\right)^{100}=125^{100}\)
Vì \(128^{100}>125^{100}\)\(\Rightarrow\)\(2^{700}>5^{300}\)
Vậy \(2^{700}>5^{300}\)
b) \(S=1+2+2^2+...+2^{50}\)
\(\Rightarrow2S=2+2^2+2^3+...+2^{51}\)
\(\Rightarrow2S-S=\left(2+2^2+2^3+...+2^{51}\right)-\left(1+2+2^2+...+2^{50}\right)\)
\(\Rightarrow S=2^{51}-1< 2^{51}\)
Vậy S < 251
_Chúc bạn học tốt_
\(2\left(x-1\right)^3-50=-300\)
\(\Leftrightarrow2\left(x-1\right)^3=-300+50\)
\(\Leftrightarrow2\left(x-1\right)^3=-250\)
\(\Leftrightarrow\left(x-1\right)^3=-250:2\)
\(\Leftrightarrow\left(x-1\right)^3=-125\)
\(\Leftrightarrow\left(x-1\right)^3=5^3\)
\(\Leftrightarrow x-1=5\)
\(\Leftrightarrow x=6\)
Vậy \(x=6\)
\(2.\left(x-1\right)^3-50=-300\)
\(\Rightarrow2.\left(x-1\right)^3=-250\)
\(\Rightarrow\left(x-1\right)^3=-125\)
\(\Rightarrow x-1=-5\)
\(\Rightarrow x=-4\)