Tìm x:
\(^{7^{x-1}-2.7^{100}=5.7^{100}}\)
\(5^{x-4}=25\)
Tính:
\(\left(2^{100}.5+2^{100}.3\right):2^{101}\)
\(3^5:3^3+2^2.2^3-14\)
Mong các bạn giúp!!!!
Những câu hỏi liên quan
c. dfrac{x-4}{5}+dfrac{3x-2}{10}-xdfrac{2x-5}{3}-dfrac{7x+2}{6}
d. left(x+2right)^3-left(x-2right)^312xleft(x-1right)-8
e. left(x+5right)left(x+2right)-3left(4x-3right)left(5-xright)^2
f. dfrac{x-5}{100}+dfrac{x-4}{101}+dfrac{x-3}{102}dfrac{x-100}{5}+dfrac{x-101}{4}+dfrac{x-102}{3}
g. dfrac{29-x}{21}+dfrac{27-x}{23}+dfrac{25-x}{25}+dfrac{23-x}{27}+dfrac{21-x}{29}5
Đọc tiếp
c. \(\dfrac{x-4}{5}+\dfrac{3x-2}{10}-x=\dfrac{2x-5}{3}-\dfrac{7x+2}{6}\)
d. \(\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-1\right)-8\)
e. \(\left(x+5\right)\left(x+2\right)-3\left(4x-3\right)=\left(5-x\right)^2\)
f. \(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)
g. \(\dfrac{29-x}{21}+\dfrac{27-x}{23}+\dfrac{25-x}{25}+\dfrac{23-x}{27}+\dfrac{21-x}{29}=5\)
d: \(\Leftrightarrow x^3+6x^2+12x+8-x^3+6x^2-12x+8=12x^2-12x-8\)
\(\Leftrightarrow12x^2+16=12x^2-12x-8\)
=>-12x=24
hay x=-2
e: \(\left(x+5\right)\left(x+2\right)-3\left(4x-3\right)=\left(x-5\right)^2\)
\(\Leftrightarrow x^2+7x+10-12x+9=x^2-10x+25\)
=>-5x+19=-10x+25
=>5x=6
hay x=6/5
f: \(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)
=>x-105=0
hay x=105
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1, Tính \(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)2,Tính \(\left(1-\frac{1}{2^2}\right)x\left(1-\frac{1}{3^2}\right)x\left(1-\frac{1}{4^2}\right)x...x\left(1-\frac{1}{n^2}\right)\)
Tính nhanh
A = 1 x 2 + 3 x 4 + 5 x 6 + ....+ 99 x 100
B = 1 × 2 x 3 + 4 x 5 x 6 + ... + 99 x 100 x 101
Giúp mk với nha các bạn
6 tháng 3 2020 lúc 14:49
1.Chứng tỏ rằng:A75.(42004+42003+...+42+4+1)+25 chia hết cho 1002.tính nhanh:Afrac{left(1+2+3+...+99+100right)left(frac{1}{2}-frac{1}{3}-frac{1}{7}-frac{1}{9}right)left(63.1,2-21.3,6right)}{1-2+3-4+...+99-100}Bfrac{left(frac{1}{14}-frac{sqrt{2}}{7}+frac{sqrt[3]{2}}{35}right).left(-frac{4}{15}right)}{left(frac{1}{10}+frac{sqrt[3]{2}}{25}-frac{sqrt{2}}{5}right).frac{5}{7}}3.a)tính giá trị của biểu thức A3x2-2x+1 với |x|frac{1}{2}b)Tìm x nguyên để sqrt{x+1}chia hết cho sqrt{x-3}
Đọc tiếp
1.Chứng tỏ rằng:
A=75.(42004+42003+...+42+4+1)+25 chia hết cho 100
2.tính nhanh:
\(A=\frac{\left(1+2+3+...+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+...+99-100}\)
\(B=\frac{\left(\frac{1}{14}-\frac{\sqrt{2}}{7}+\frac{\sqrt[3]{2}}{35}\right).\left(-\frac{4}{15}\right)}{\left(\frac{1}{10}+\frac{\sqrt[3]{2}}{25}-\frac{\sqrt{2}}{5}\right).\frac{5}{7}}\)
3.a)tính giá trị của biểu thức A=3x2-2x+1 với |x|=\(\frac{1}{2}\)
b)Tìm x nguyên để \(\sqrt{x+1}\)chia hết cho \(\sqrt{x-3}\)
1. A = 75(42004 + 42003 +...+ 42 + 4 + 1) + 25
A = 25 . [3 . (42004 + 42003 +...+ 42 + 4 + 1) + 1]
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 3 + 1)
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 4)
A = 25 . 4 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1)
A =100 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1) \(⋮\) 100
3a) |x| = 1/2
=> x = 1/2 hoặc x = -1/2
với x = 1/2:
A = \(3.\left(\frac{1}{2}\right)^2-2.\frac{1}{2}+1\)
\(A=\frac{3}{4}-1+1=\frac{3}{4}\)
với x = -1/2
A = \(3.\left(-\frac{1}{2}\right)^2-2\left(-\frac{1}{2}\right)+1\)
\(A=\frac{3}{4}+1+1=\frac{3}{4}+2=\frac{11}{4}\)
2.
A=\(\frac{\left(1+2+3+.....+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+......+99-100}\)\
A=0
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1) giải pt :
a) dfrac{x-5}{100}+dfrac{x-4}{101}+dfrac{x-3}{102}dfrac{x-100}{5}+dfrac{x-101}{4}+dfrac{x-102}{3}
b) dfrac{29-x}{21}+dfrac{27-x}{23}+dfrac{25-x}{25}+dfrac{23-x}{27}+dfrac{21-x}{29}-5
2) giải pt :
a) left(5x+1right)^2left(3x-2right)^2
b) left(x+2right)^3left(2x+1right)^3
c) left(x+3right)^4+left(x+5right)^42
d) x^4-3x^3+4x^2-3x+10
Đọc tiếp
1) giải pt :
a) \(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)
b) \(\dfrac{29-x}{21}+\dfrac{27-x}{23}+\dfrac{25-x}{25}+\dfrac{23-x}{27}+\dfrac{21-x}{29}=-5\)
2) giải pt :
a) \(\left(5x+1\right)^2=\left(3x-2\right)^2\)
b) \(\left(x+2\right)^3=\left(2x+1\right)^3\)
c) \(\left(x+3\right)^4+\left(x+5\right)^4=2\)
d) \(x^4-3x^3+4x^2-3x+1=0\)
1)
\(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)
\(\Leftrightarrow\dfrac{x-5}{100}+1+\dfrac{x-4}{101}+1+\dfrac{x-3}{102}+1=\dfrac{x-100}{5}+1+\dfrac{x-101}{4}+1+\dfrac{x-102}{3}+1\)
\(\Leftrightarrow\dfrac{x-105}{100}+\dfrac{x-105}{101}+\dfrac{x-105}{102}=\dfrac{x-105}{5}+\dfrac{x-105}{4}+\dfrac{x-105}{3}+\dfrac{x-105}{2}\)
\(\Leftrightarrow\dfrac{x-105}{100}+\dfrac{x-105}{101}+\dfrac{x-105}{102}-\dfrac{x-105}{5}-\dfrac{x-105}{4}-\dfrac{x-105}{3}-\dfrac{x-105}{2}=0\)
\(\Leftrightarrow\left(x-105\right)\left(\dfrac{1}{100}+\dfrac{1}{101}+\dfrac{1}{102}-\dfrac{1}{5}-\dfrac{1}{4}-\dfrac{1}{3}-\dfrac{1}{2}\right)=0\)\(\Leftrightarrow105-x=0\)
\(\Leftrightarrow x=105\)
b)
\(\dfrac{29-x}{21}+\dfrac{27-x}{23}+\dfrac{25-x}{25}+\dfrac{23-x}{27}+\dfrac{21-x}{29}=0\)
\(\Leftrightarrow\dfrac{29-x}{21}+1+\dfrac{27-x}{23}+1+\dfrac{25-x}{25}+1+\dfrac{23-x}{27}+1+\dfrac{21-x}{29}+1=0\)
\(\Leftrightarrow\dfrac{50-x}{21}+\dfrac{50-x}{23}+\dfrac{50-x}{25}+\dfrac{20-x}{27}+\dfrac{50-x}{29}=0\)
\(\Leftrightarrow\left(50-x\right)\left(\dfrac{1}{21}+\dfrac{1}{23}+\dfrac{1}{25}+\dfrac{1}{27}+\dfrac{1}{29}\right)=0\)
\(\Leftrightarrow50-x=0\)
\(\Leftrightarrow x=50\)
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2)
\(\left(5x+1\right)^2=\left(3x-2\right)^2\)
\(\Leftrightarrow\left|5x+1\right|=\left|3x-2\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+1=3x-2\\5x+1=-3x+2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-3}{2}\\x=\dfrac{1}{8}\end{matrix}\right.\)
b) \(\left(x+2\right)^3=\left(2x+1\right)^3\)
\(\Leftrightarrow x^3+6x^2+12x+8=8x^3+12x^2+6x+1\)
\(\Leftrightarrow-7x^3-6x^2+6x+7=0\)
\(\Leftrightarrow-7x^3+7x^2-13x^2+13x-7x+7=0\)
\(\Leftrightarrow-7x^2\left(x-1\right)-13x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-7x^2-13x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\-7x^2-13x-7=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\-7\left(x^2+\dfrac{13}{7}x+1\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\-7\left(x+\dfrac{13}{14}\right)^2-\dfrac{169}{196}=0\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow x=1\)
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c. \(\left(x+3\right)^4+\left(x+5\right)^4=2\)
Đặt: \(y=x+4\), ta có:
\(\left(y-1\right)^4+\left(y+1\right)^4=2\)
\(\Leftrightarrow y^4-4y^3+6y^2-4y+1+y^4+4y^3+6y^2+4y+1=2\)
\(\Leftrightarrow2y^4+12y^2=0\)
\(\Leftrightarrow2y^2\left(y^2+6\right)=0\)
\(\Leftrightarrow y=0\)
\(\Leftrightarrow x=-4\)
d) \(x^4-3x^3+4x^2-3x+1=0\)
\(\Leftrightarrow x^4-x^3-2x^3+2x^2+2x^2-2x-x+1=0\)
\(\Leftrightarrow x^3\left(x-1\right)-2x^2\left(x-1\right)+2x\left(x-1\right)-\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-2x^2+2x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-x^2-x^2+x+x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-1\right)-x\left(x-1\right)+\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(x^2-x+1\right)=0\)
\(\Leftrightarrow x=1\)
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Tính
a) (x-1/2)+(x-1/4)+(x-1/8)+...+(x-1/512)
Tìm x
a) (x-1/1×2)+(x-1/2×3)+...+(x-1/100×101)
b) (x-1)+(x-2)+(x-3)+...+(x-101)=5050
c) x+1/2+1/3+1/4+...+1/100=3/2+4/3+5/4++...+101/100
19 tháng 12 2021 lúc 20:48
\(\left(x+2\right)-26=\left(4^3-3^2.7\right)^{100}\)
Tìm x
a/\(^{3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]}\)
b/(x+1)+(x+2)+(x+3)+....+(x+100)=205550
c/Ix-5I=18+2x(-8)
d/\(\left(3x-2^4\right).7^5=2.7^6.\frac{1}{2009^0}\)
b/100x+(1+2+3+...+100)=205550
100x+5050=205550
100x=205550-5050
100x=200500
x=200500/100
x=2005
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d/(3x-24).75=2.76.1/20090
(3x-24).75=2.76.1
(3x-24)=2.76:75
(3x-24)=2.7
3x-16=14
3x=14+16
3x=30
x=30/10=3
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b) ( \(x\)+ 1 ) + ( \(x\)+ 2 ) + ( \(x\)+ 3 ) + ... + ( \(x\)+ 100 ) = 205550
\(x\)x 100 + ( 1 + 2 + 3 + ... + 100 ) = 205550
\(x\)x 100 + 5050 = 205550
\(x\)x 100 = 205550 - 5050
\(x\)x 100 = 200500
\(x\)= 200500 : 100
\(x\)= 2005
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Xem thêm câu trả lời
tính
Xem chi tiết
\(\left[\frac{100}{3}\right]+\left[\frac{100}{3^2}\right]+\left[\frac{100}{3^3}\right]\left[\frac{100}{3^4}\right]\)
Tìm x,y\(\frac{5}{x}+\frac{y}{4}=\frac{1}{8}\)
Ta có :5/x = 1/8 - y/4 = (1-2y)/8
<=> x = 5.8/(1-2y) ; thấy 1-2y là số lẻ nên ƯCLN(8,1-2y) = 1
do đó x/8 = 5/(1-2y)
Để x, y nguyên khi 1-2y phải là ước của 5
*Xét 1-2y = -1 => y = 1 => x = -40
*Xét 1-2y = 1 => y = 0 => x = 40
*Xét 1-2y = -5 => y = 3 => x = -8
*Xét 1-2y = 5 => y = -2 => x = 8
Vậy có 4 cặp (x,y) nguyên (-40,1) ; (40, 0) ; (-8, -5) ; (8, 5)
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