so sánh
a, A = ( 1 - 1/2 ) x ( 1 - 1/3 ) x .....x ( 1 - 1/19 ) x ( 1 - 1/20 )
So sánh A vs 1/21
b, B = ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16 ) x .....x ( 1 - 1/81 ) x ( 1 - 1/100 )
So sánh B vs 11/21
So sánh B = (1/4 -1) x (1/9 -1) x ( 1/16 -1) x ... x (1/81 -1) x (1/100 -1) với -11/21
1)tìm x
a)(1/3-5/6.x)^3+21/54=5/6
b)1/12-1/3(1/2.x-1)^4=1/16
c)(3/5)^x-1+5.(3/5)^x-1=54/25
d)(2/3)^x+(2/3)^x+2=101/243
2) so sánh
a)1/27^11 và 1/81^8
b)1/3^99 và 1/11^21
a) => \(\left(\frac{1}{3}-\frac{5}{6}x\right)^3=\frac{5}{6}-\frac{21}{54}=\frac{24}{54}=\frac{4}{9}\)
=> \(\frac{1}{3}-\frac{5}{6}x=\sqrt[3]{\frac{4}{9}}\) => \(\frac{5}{6}x=\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\) => \(x=\frac{6}{5}.\left(\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\right)\)
b) \(\frac{1}{3}\left(\frac{1}{2}x-1\right)^4=\frac{1}{12}-\frac{1}{16}=\frac{1}{48}\) => \(\left(\frac{1}{2}x-1\right)^4=\frac{3}{48}=\frac{1}{16}\)
=> \(\frac{1}{2}x-1=\frac{1}{2}\) hoặc \(\frac{1}{2}x-1=-\frac{1}{2}\)
=> \(\frac{1}{2}x=\frac{3}{2}\) hoặc \(\frac{1}{2}x=\frac{1}{2}\) => x = 3 hoặc x = 1
c) \(\left(1+5\right).\left(\frac{3}{5}\right)^{x-1}=\frac{54}{25}\) => \(\left(\frac{3}{5}\right)^{x-1}=\frac{9}{25}=\left(\frac{3}{5}\right)^2\)
=> x - 1= 2 => x = 3
d) \(\left(1+\left(\frac{2}{3}\right)^2\right).\left(\frac{2}{3}\right)^x=\frac{101}{243}\) => \(\frac{13}{9}.\left(\frac{2}{3}\right)^x=\frac{101}{243}\)
=> \(\left(\frac{2}{3}\right)^x=\frac{101}{243}:\frac{13}{9}=\frac{101}{351}\) (có lẽ đề sai)
2) \(\frac{1}{27^{11}}=\frac{1}{\left(3^3\right)^{11}}=\frac{1}{3^{33}}\); \(\frac{1}{81^8}=\frac{1}{\left(3^4\right)^8}=\frac{1}{3^{32}}\)
Vì 333 > 332 => \(\frac{1}{3^{33}}\) < \(\frac{1}{3^{32}}\) => \(\frac{1}{27^{11}}\) < \(\frac{1}{81^8}\)
b) \(\frac{1}{3^{99}}=\frac{1}{\left(3^3\right)^{33}}=\frac{1}{27^{33}}
1)tìm x
a)(1/3-5/6.x)^3+21/54=5/6
b)1/12-1/3(1/2.x-1)^4=1/16
c)(3/5)^x-1+5.(3/5)^x-1=54/25
d)(2/3)^x+(2/3)^x+2=101/243
2) so sánh
a)1/27^11 và 1/81^8
b)1/3^99 và 1/11^21
A=(1/4-1)x(1/9-1 )x(1/16-1)...(1/400-1) so sánh vs -1/2
Ta có A=\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)....\left(\frac{1}{400}-1\right)\)
=\(\frac{-3}{2^2}.\frac{-8}{3^2}.\frac{-15}{4^2}...\frac{-399}{20^2}\)
=\(\frac{-\left(1.3\right)}{2.2}.\frac{-\left(2.4\right)}{3.3}.\frac{-\left(3.5\right)}{4.4}....\frac{-\left(19.21\right)}{20.20}\)
=\(-\left(\frac{1.2.3...19}{2.3.4...20}.\frac{3.4.5...21}{2.3.4...20}\right)\)
=\(-\left(\frac{1}{20}.\frac{21}{2}\right)=-\frac{21}{40}< -\frac{21}{42}=-\frac{1}{2}\)
Cho 2 biểu thức:
A= (1-1/2).(1-1/3).(1-1/4) .... (1-1/19).(1-1/20)
B= (1-1/4).(1-1/9).(1-1/16) ... (1-1/81).(1-1/100)
a) Rút gọn biểu thức A, B
b) So sánh biểu thức A với 1/21
So sánh biểu thức B với 11/21
a) Cho S= 1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20
so sánh với 1/2
b) -2/x=y/3 và x<0<y
c) x-3/ y-3=3/2 và x-y=4
TL :
Đây nhé
HT
@@@@@@@@@@@@@@@@@
a)Tìm các số nguyên x,y biết (x-3)(y-3) = 9
b)So sánh hai phân số A = 10^19 + 1/10^20 + 1 ; B = 10^20 + 1/10^21 + 1
a) (x - 3)(y - 3) = 9 = 1.9 = 3.3
Lập bảng:
x - 3 | 1 | -1 | 3 | -3 | 9 | -9 |
y - 3 | 9 | -9 | 3 | -3 | 1 | -1 |
x | 4 | 2 | 6 | 0 | 12 | -3 |
y | 12 | -6 | 6 | 0 | 4 | 2 |
Vậy ...
b) A = \(\frac{10^{19}+1}{10^{20}+1}\) => 10A = \(\frac{10^{20}+10}{10^{20}+1}=1+\frac{9}{10^{20}+1}\)
B = \(\frac{10^{20}+1}{10^{21}+1}\) => 10B = \(\frac{10^{21}+10}{10^{21}+1}=1+\frac{9}{10^{21}+1}\)
Do \(10^{20}+1< 10^{21}+1\) => \(\frac{9}{10^{20}+1}>\frac{9}{10^{21}+1}\) => 10A > 10B => A > B
Bài 1 : không tính hãy so sánh
a, (-16) . 4 với (-37)
b, -19 . (- 3) với -56
c, ( - 66) . 2 với - 124
d, ( - 91) . 3 với - 233
bài 2 : tìm x thuộc Z
a, ( - 31 ) .x = - 93
b,( - 4 ) .x = - 20
c , 5 . x + 1 = - 4
d, -12 . x + 1 = -4
bài 3
a, x . ( x+ 9 ) = 0
b , (x - 5 )2 = 9
c, ( 7 - x )2 = - 64
bài 4 : tìm x,y thuộc Z biết
a, x.y = - 2
b, ( x - 1) . ( y + 2 ) = - 3
Bài 4:
a: xy=-2
=>\(x\cdot y=1\cdot\left(-2\right)=\left(-2\right)\cdot1=\left(-1\right)\cdot2=2\cdot\left(-1\right)\)
=>\(\left(x,y\right)\in\left\{\left(1;-2\right);\left(-2;1\right);\left(-1;2\right);\left(2;-1\right)\right\}\)
b: \(\left(x-1\right)\left(y+2\right)=-3\)
=>\(\left(x-1\right)\cdot\left(y+2\right)=1\cdot\left(-3\right)=\left(-3\right)\cdot1=-1\cdot3=3\cdot\left(-1\right)\)
=>\(\left(x-1;y+2\right)\in\left\{\left(1;-3\right);\left(-3;1\right);\left(-1;3\right);\left(3;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(2;-5\right);\left(-2;-1\right);\left(0;1\right);\left(4;-3\right)\right\}\)
Bài 3:
a: \(x\left(x+9\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x+9=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=0\\x=-9\end{matrix}\right.\)
b: \(\left(x-5\right)^2=9\)
=>\(\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=3+5=8\\x=-3+5=2\end{matrix}\right.\)
c: \(\left(7-x\right)^2=-64\)
mà \(\left(7-x\right)^2>=0\forall x\)
nên \(x\in\varnothing\)
Bài 2:
a: \(\left(-31\right)\cdot x=-93\)
=>\(31\cdot x=93\)
=>\(x=\dfrac{93}{31}=3\)
b: \(\left(-4\right)\cdot x=-20\)
=>\(4\cdot x=20\)
=>\(x=\dfrac{20}{4}=5\)
c: \(5x+1=-4\)
=>\(5x=-4-1=-5\)
=>\(x=-\dfrac{5}{5}=-1\)
d: \(-12x+1=-4\)
=>\(-12x=-4-1=-5\)
=>\(12x=5\)
=>\(x=\dfrac{5}{12}\)
Cho 2 biểu thức:
A= (1-1/2).(1-1/3).(1-1/4) .... (1-1/19).(1-1/20)
B= (1-1/4).(1-1/9).(1-1/16) ... (1-1/81).(1-1/100)
a) Rút gọn biểu thức A, B
b) So sánh biểu thức A với 1/21
So sánh biểu thức B với 11/21
ai nhanh chế tik