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Bài 3:
a: \(S=1+5^2+5^4+\cdots+5^{200}\)
=>25S=\(5^2+5^4+5^6+\cdots+5^{202}\)
=>25S-S=\(5^2+5^4+\cdots+5^{202}-1-5^2-\cdots-5^{200}\)
=>24S=\(5^{202}-1\)
=>\(S=\frac{5^{202}-1}{24}\)
b: \(4^{30}=\left(2^2\right)^{30}=2^{60}=2^{30}\cdot2^{30}=8^{10}\cdot4^{15}\)
\(3\cdot24^{10}=3\cdot3^{10}\cdot8^{10}=8^{10}\cdot3^{11}\)
mà \(4^{15}>3^{11}\)
nên \(4^{30}>3\cdot24^{10}\)
=>\(2^{30}+3^{30}+4^{30}>3\cdot24^{10}\)
Bài 2:
a: |2x-3|>5
=>\(\left[\begin{array}{l}2x-3>5\\ 2x-3<-5\end{array}\right.\Rightarrow\left[\begin{array}{l}2x>8\\ 2x<-2\end{array}\right.\Rightarrow\left[\begin{array}{l}x>4\\ x<-1\end{array}\right.\)
c: |3x-1|<=7
=>-7<=3x-1<=7
=>-6<=3x<=8
=>\(-2\le x\le\frac83\)
d: \(\left|3x-5\right|+\left|2x+3\right|=7\) (1)
TH1: \(x<-\frac32\)
=>2x+3<0; 3x-5<0
(1) sẽ trở thành: -2x-3-3x+5=7
=>-5x+2=7
=>-5x=5
=>x=-1(loại)
TH2: -3/2<=x<5/3
=>2x+3>=0; 3x-5<0
(1) sẽ trở thành: 2x+3-3x+5=7
=>-x+8=7
=>-x=-1
=>x=-1(nhận)
TH3: x>=5/3
=>2x+3>0; 3x-5>=0
(1) sẽ trở thành: 2x+3+3x-5=7
=>5x-2=7
=>5x=9
=>x=9/5(nhận)
Noob ơi, bạn phải đưa vào máy tính ý solve cái là ra x luôn, chỉ tội là đợi hơi lâu
a, 4.(18 - 5x) - 12(3x - 7) = 15(2x - 16) - 6(x + 14)
=> 72 - 20x - 36x + 84 = 30x - 240 - 6x - 84
=> (72 + 84) + (-20x - 36x) = (30x - 6x) + (-240 - 84)
=> 156 - 56x = 24x - 324
=> 24x + 56x = 324 + 156
=> 80x = 480
=> x = 480 : 80 = 6
Vậy x = 6
Bài 2:
\(\dfrac{a+b}{a-b}=\dfrac{c+a}{c-a}\)
\(\Rightarrow\dfrac{a+b}{c+a}=\dfrac{a-b}{c-a}=\dfrac{a+b+a-b}{c+a+c-a}=\dfrac{a}{c}\) (T/c dãy tỷ số = nhau)
\(\Rightarrow\dfrac{a+b}{c+a}=\dfrac{a}{c}\Rightarrow c\left(a+b\right)=a\left(c+a\right)\)
\(\Rightarrow ac+bc=ac+a^2\Rightarrow a^2=bc\)
\(a,\left(\frac{3}{8}+-\frac{3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
= \(\left(-\frac{3}{8}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
= \(\frac{5}{24}:\frac{5}{6}+\frac{1}{2}\)
= \(\frac{1}{4}+\frac{1}{2}\)
= \(\frac{3}{4}\)
b)\(-\frac{7}{3}.\frac{5}{9}+\frac{4}{9}.\left(-\frac{3}{7}\right)+\frac{17}{7}\)
=\(-\frac{35}{27}+\left(-\frac{4}{21}\right)+\frac{17}{7}\)
= \(-\frac{35}{27}+\frac{47}{21}\)
= \(\frac{178}{189}\)
c) \(\frac{117}{13}-\left(\frac{2}{5}+\frac{57}{13}\right)\)
= \(\frac{117}{13}-\frac{311}{65}\)
= \(\frac{274}{65}\)
d) \(\frac{2}{3}-0,25:\frac{3}{4}+\frac{5}{8}.4\)
= \(\frac{2}{3}-\frac{1}{4}:\frac{3}{4}+\frac{5}{8}.4\)
= \(\frac{2}{3}-\frac{1}{3}+\frac{5}{2}\)
= \(\frac{1}{3}+\frac{5}{2}\)
= \(\frac{17}{6}\)
1.
a) \(\frac{-7}{9}.2\frac{3}{4}=\frac{-7}{9}.\frac{11}{4}=\frac{-77}{36}\)
b) \(\frac{2}{3}+\frac{1}{3}.\frac{-2}{5}=\frac{2}{3}+\frac{-2}{15}=\frac{8}{15}\)
c) \(\frac{3}{4}.15\frac{1}{3}-\frac{3}{4}.43\frac{1}{3}=\frac{3}{4}.\frac{46}{3}-\frac{3}{4}.\frac{130}{3}=\frac{23}{2}-\frac{65}{2}=-21\)
d) \(\left(-49,1\right).\frac{13}{27}-58,9.\frac{13}{27}=\frac{13}{27}.\left(-49,1-58,9\right)=\frac{13}{27}.\left(-108\right)=-52\)
e) \(0,375:\left(-4,5\right)=\frac{-1}{12}\)
f) \(3\frac{1}{7}:\left(-1\frac{3}{7}\right)=\frac{22}{7}:\frac{-10}{7}=\frac{-11}{5}\)
g) \(9\frac{1}{3}:4\frac{2}{3}-2=\frac{28}{3}:\frac{14}{3}-2=2-2=0\)
h) \(\left(7\frac{3}{4}:0,3125+4,5.2\frac{2}{45}\right):\left(-8,5\right)=\left(\frac{31}{4}:\frac{5}{16}+\frac{9}{2}.\frac{92}{45}\right):\frac{-17}{2}=\left(\frac{124}{5}+\frac{46}{5}\right):\frac{-17}{2}=34:\frac{-17}{2}=-4\)
Bài 1 : Tính:
a)
\(\frac{-7}{9}.2\frac{3}{4}=\frac{-7}{9}.\frac{11}{4}=\frac{-77}{36}\)
b)
\(\frac{2}{3}+\frac{1}{3}.\frac{-2}{5}=\frac{2}{3}+\frac{-2}{15}=\frac{10}{15}+\frac{-2}{15}=\frac{8}{15}\)
c)
\(\frac{3}{4}.15\frac{1}{3}-\frac{3}{4}.43\frac{1}{3}=\frac{3}{4}.\frac{46}{3}-\frac{3}{4}.\frac{130}{3}\)\(=\frac{23}{2}-\frac{65}{2}=\frac{-42}{2}=-21\)
....
Tự lm tiếp dạng như v
Bài 2 :
\(A=\frac{-6}{11}.\frac{7}{10}.\frac{11}{-6}.-20=\left(\frac{-6}{11}.\frac{11}{-6}\right).\left(\frac{7}{10}.-20\right)\)\(=1.\left(-14\right)=-14\)
.....
Bài 3 :
\(\frac{3}{7}.x-\frac{2}{5}.x=\frac{-17}{35}\)
\(\Leftrightarrow\frac{3}{7}-\frac{2}{5}.x=\frac{-17}{35}\)
\(\Leftrightarrow\frac{1}{35}x=\frac{-17}{35}\)
\(\Leftrightarrow x=\frac{-17}{35}:\frac{1}{35}\)
\(\Leftrightarrow x=\frac{-17}{35}.35=-17\)
a) 1/4(x-3)+2=1/5
1/4.(x-3) = 1/5-2
1/4.(x-3) = -9/5
x-3 = (-9/5):1/4
x-3 = -36/5
x = -36/5+3
x= -21/5
a, \(\dfrac{1}{7}\) x ( \(\dfrac{4}{3}\))2 - \(\dfrac{1}{7}\) : \(\dfrac{9}{11}\)
= \(\dfrac{1}{7}\) x \(\dfrac{16}{9}\) - \(\dfrac{1}{7}\) x \(\dfrac{11}{9}\)
= \(\dfrac{1}{7}\) x ( \(\dfrac{16}{9}-\dfrac{11}{9}\))
= \(\dfrac{1}{7}\) x \(\dfrac{5}{9}\)
= \(\dfrac{5}{63}\)
b, 2x + \(\dfrac{1}{4}\) = \(\dfrac{3}{5}\)
2x = \(\dfrac{3}{5}-\dfrac{1}{4}\)
2x = \(\dfrac{7}{20}\)
x = \(\dfrac{7}{20}:2\)
x = \(\dfrac{7}{40}\)