Operation of Indices
HỦY DIỆT THE WORLD
09/02/2018 at 21:26-
FA KAKALOTS 09/02/2018 at 21:34
We have :
\(=\dfrac{x+2}{89}+1+\dfrac{x+5}{86}+1>\dfrac{x+8}{83}+1+\dfrac{x+11}{80}+1\)
\(=\dfrac{x+91}{89}+\dfrac{x+91}{86}>\dfrac{x+91}{83}+\dfrac{x+91}{80}\)
\(=\dfrac{x+91}{89}+\dfrac{x+91}{86}-\dfrac{x+91}{83}-\dfrac{x+91}{80}>0\)
\(=\left(x+91\right)\left(\dfrac{1}{89}+\dfrac{1}{86}-\dfrac{1}{83}-\dfrac{1}{80}\right)>0\)
To \(\dfrac{1}{89}+\dfrac{1}{86}-\dfrac{1}{83}-\dfrac{1}{80}\) different 0
\(=x+91>0\)\(=x< -91\)
HỦY DIỆT THE WORLD selected this answer. -
Fc Alan Walker 10/02/2018 at 14:16
e have :
=x+289+1+x+586+1>x+883+1+x+1180+1
=x+9189+x+9186>x+9183+x+9180
=x+9189+x+9186−x+9183−x+9180>0
=(x+91)(189+186−183−180)>0
To 189+186−183−180
different 0
=x+91>0=x<−91
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FA KAKALOTS 06/02/2018 at 12:28
a + b = 5
<=> (a+b)3=125
<=> a3 + 3a2b + 3ab2 + b3 = 125
<=> 3ab(a + b) + 35 = 125 (a3 + b3 = 35)
<=> 15ab = 90 (a + b = 5)
<=> ab = 6
a + b = 5
<=> (a + b)2 = 25
<=> a2 + 2ab + b2 = 25
<=> a2 + 12 + b2 = 25
<=> a2 + b2 = 13
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Hồ Thu Giang 19/03/2017 at 14:26
a + b = 5
<=> \(\left(a+b\right)^3=125\) <=> a3 + 3a2b + 3ab2 + b3 = 125
<=> 3ab(a + b) + 35 = 125 (a3 + b3 = 35)
<=> 15ab = 90 (a + b = 5)
<=> ab = 6
a + b = 5
<=> (a + b)2 = 25
<=> a2 + 2ab + b2 = 25
<=> a2 + 12 + b2 = 25
<=> a2 + b2 = 13
Lionel Messi
19/03/2017 at 11:52-
FA KAKALOTS 06/02/2018 at 12:29
We have : (x + y)2 - (x - y)2 = 18 - 12
(x2 + 2xy + y2) - (x2 - 2xy + y2) = 6
4xy = 6
2xy = 3
=> x2 + y2 = 18 - 3 = 15
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We have : (x + y)2 - (x - y)2 = 18 - 12
(x2 + 2xy + y2) - (x2 - 2xy + y2) = 6
4xy = 6
2xy = 3
=> x2 + y2 = 18 - 3 = 15
Lionel Messi
19/03/2017 at 11:51-
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\(3^{3x+2y}=3^{3x}\times3^{2y}=\left(3^x\right)^3\times\left(3^y\right)^2=\left(\dfrac{2}{9}\right)^3\times27^2\)
\(=\dfrac{2^3\times3^6}{3^6}=8\)
Lionel Messi
19/03/2017 at 11:50-
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We have : (2x2 + 1)(5x + 2) = 10x3 + 4x2 + 5x + 2
So a = 4
Lionel Messi
19/03/2017 at 11:49-
FA KAKALOTS 06/02/2018 at 12:29
(a) 5m.252m = 1252m - 1
=> 5m.54m = (53)2m - 1
=> 55m = 56m - 3
=> 5m = 6m - 3
=> m = 3
(b) 5m.25m.125m.625m = 530
=> (5.25.125.625)m = 530
=> (5.52.53.54)m = 530
=> 510m = 530
=> 10m = 30
=> m = 3
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(a) 5m.252m = 1252m - 1
=> 5m.54m = (53)2m - 1
=> 55m = 56m - 3
=> 5m = 6m - 3
=> m = 3
(b) 5m.25m.125m.625m = 530
=> (5.25.125.625)m = 530
=> (5.52.53.54)m = 530
=> 510m = 530
=> 10m = 30
=> m = 3
Lionel Messi
19/03/2017 at 11:47-
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Because \(5x^2-4x=5x^2-4x\) and \(2>-3\) => a > b
You are right (True).
Lionel Messi
19/03/2017 at 11:45Lionel Messi
19/03/2017 at 11:43-
FA KAKALOTS 06/02/2018 at 12:30
(x + y)2 = 9
<=> x2 + 2xy + y2 = 9 (1)
(x - y)2 = 1
<=> x2 - 2xy + y2 = 1 (2)
(1) - (2) => 4xy = 8 => xy = 2
=> x2 + 2xy + y2 = 9
<=> x2 + 4 + y2 = 9
<=> x2 + y2 = 5
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Hồ Thu Giang 19/03/2017 at 14:36
(x + y)2 = 9
<=> x2 + 2xy + y2 = 9 (1)
(x - y)2 = 1
<=> x2 - 2xy + y2 = 1 (2)
(1) - (2) => 4xy = 8 => xy = 2
=> x2 + 2xy + y2 = 9
<=> x2 + 4 + y2 = 9
<=> x2 + y2 = 5
Lionel Messi
19/03/2017 at 11:42Lionel Messi
19/03/2017 at 11:41-
FA KAKALOTS 06/02/2018 at 12:30
We have : 725 = (74)6.7
The units digit of 74 is 1 (74 = 2401),so the units digit of (74)6 is 1
=> The units digit of 725 is 7
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We have : 725 = (74)6.7
The units digit of 74 is 1 (74 = 2401),so the units digit of (74)6 is 1
=> The units digit of 725 is 7
steve jobs
18/03/2017 at 10:15-
mathlove 18/03/2017 at 11:04
By the assumption \(\left\{{}\begin{matrix}a+b=4\\a^3+b^3=28\end{matrix}\right.\Rightarrow a^2-ab+b^2=\dfrac{28}{4}=7\Rightarrow2a^2-2ab+2b^2=14\).
Other hand, \(a+b=4\Rightarrow a^2+2ab+b^2=16\). So:
\(3\left(a^2+b^2\right)=\left(2a^2-2ab+2b^2\right)+\left(a^2+2ab+b^2\right)=14+16\Rightarrow a^2+b^2=10\)
steve jobs selected this answer. -
FA KAKALOTS 06/02/2018 at 12:30
By the assumption {a+b=4a3+b3=28⇒a2−ab+b2=284=7⇒2a2−2ab+2b2=14
.
Other hand, a+b=4⇒a2+2ab+b2=16
. So:
3(a2+b2)=(2a2−2ab+2b2)+(a2+2ab+b2)=14+16⇒a2+b2=10
steve jobs
18/03/2017 at 10:12-
mathlove 18/03/2017 at 11:05
\(m^2+n^2=\left(m+n\right)^2-2mn=103\)
steve jobs selected this answer. -
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steve jobs
18/03/2017 at 10:10-
mathlove 18/03/2017 at 10:37
\(27^x.243^y=\left(3^3\right)^x\left(3^5\right)^y=3^{\left(3x+5y\right)}=3^2=9\)
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FA KAKALOTS 06/02/2018 at 12:31
27x.243y=(33)x(35)y=3(3x+5y)=32=9
steve jobs
18/03/2017 at 10:09-
mathlove 18/03/2017 at 10:43
We have \(a^m=\dfrac{1}{3},a^n=6\Rightarrow2=6.\dfrac{1}{3}=a^n.a^m=a^{m+n}\), so
\(2^{2m+3n}=\left(a^{m+n}\right)^{2m+3n}=a^{\left(m+n\right)\left(2m+3n\right)}\) .
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FA KAKALOTS 06/02/2018 at 12:31
We have am=13,an=6⇒2=6.13=an.am=am+n
, so
22m+3n=(am+n)2m+3n=a(m+n)(2m+3n)
.
steve jobs
18/03/2017 at 10:07-
mathlove 18/03/2017 at 10:52
Put \(a=2^{777},b=3^{555},c=4^{444}\). We have :
\(a=2^{777}=\left(2^7\right)^{111}=128^{111},b=3^{555}=\left(3^5\right)^{111}=243^{111},c=4^{444}=\left(4^4\right)^{111}=256^{111}\Rightarrow a< b< c\).
So: \(2^{777}< 3^{555}< 4^{444}\).
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FA KAKALOTS 06/02/2018 at 12:31
Put a=2777,b=3555,c=4444
. We have :
a=2777=(27)111=128111,b=3555=(35)111=243111,c=4444=(44)111=256111⇒a<b<c
.
So: 2777<3555<4444
.
steve jobs
18/03/2017 at 10:04-
mathlove 18/03/2017 at 11:13
a) \(3^x=243=3^5\Leftrightarrow x=5\).
b) \(5^m=625\Leftrightarrow5^m=5^4\Leftrightarrow m=4\).
c) By \(16^x.5^{2x}=16^x.25^x=\left(16.25\right)^x=400^x\), so the done equation equivalant to
\(400^x=400^1\Leftrightarrow x=1\).
d) \(2^{2n+2}+2^{2n}=160\Leftrightarrow2^{2n}\left(2^2+1\right)=160\Leftrightarrow2^{2n}=2^5\Leftrightarrow2n=5\Leftrightarrow n=2,5.\)
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FA KAKALOTS 06/02/2018 at 12:32
a) 3x=243=35⇔x=5
.
b) 5m=625⇔5m=54⇔m=4
.
c) By 16x.52x=16x.25x=(16.25)x=400x
, so the done equation equivalant to
400x=4001⇔x=1
.
d) 22n+2+22n=160⇔22n(22+1)=160⇔22n=25⇔2n=5⇔n=2,5.
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Hạo Nam 24/03/2017 at 17:56a) 3x=243=35⇔x=5.
b) 5m=625⇔5m=54⇔m=4.
c) By 16x.52x=16x.25x=(16.25)x=400x, so the done equation equivalant to
400x=4001⇔x=1.
d) 22n+2+22n=160⇔22n(22+1)=160⇔22n=25⇔2n=5⇔n=2,5.
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