P=24(7^2+1)(7^4+1)(7^8+1)(7^16+1)
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10 tháng 11 2017
\(\text{a) }\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\dfrac{3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ \\ =\dfrac{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{\left(2^{16}-1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{2^{32}-1}{3}\\ \)
\(\text{b) }24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right) \\ =\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^{16}-1\right)\left(5^{16}+1\right)\\ =5^{32}-1\\ \)
\(\text{c) }48\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^2-1\right)\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^4-1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^8-1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^{16}-1\right)\left(7^{16}+1\right)\\ =7^{32}-1\)
NN
3
16 tháng 4 2022
2/5 + 11/15 = 17/15
7/8 - 7/9 = 7/72
11/13 x 26/31 = 22/31
16/24 : 4 = 1/6
30 : 6/5 = 25
9/16 : 4 = 9/64
1/2 : 1/3 x 8/15 = 3/2 x 8/15 = 4/5
TN
6 tháng 8 2018
\(1\frac{1}{2}+x=\frac{3}{2}-7\)
<=> \(\frac{3}{2}+x=\frac{-11}{2}\)
<=> \(x=-7\)
\(\frac{1}{4}+\frac{1}{3}:3x=-5\)
<=> \(\frac{1}{3}:3x=\frac{-21}{4}\)
<=> \(3x=\frac{-4}{63}\)
<=> \(x=\frac{4}{189}\)
\(\frac{4}{5}.x=\frac{8}{35}\)
<=> \(x=\frac{2}{7}\)
\(\frac{2}{3x}-\frac{1}{4}=\frac{7}{1}\)
<=> \(\frac{2}{3x}=\frac{29}{4}\)
=> \(8=87x\)
<=> \(x=\frac{8}{87}\)
\(\frac{3}{5x}+\frac{1}{2}=\frac{1}{7}\)
<=> \(\frac{3}{5x}=\frac{-5}{14}\)
<=> \(-25x=42\)
<=> \(x=\frac{-42}{25}\)
\(1-\left(5\frac{3}{8}+x-7\frac{5}{24}\right):\left(-16.\frac{2}{3}\right)=0\)
<=> \(1-\left(\frac{43}{8}+x-\frac{173}{24}\right):\frac{-32}{3}=0\)
<=> \(\frac{43}{8}+x-\frac{173}{24}=\frac{-32}{3}\)
<=> \(\frac{43}{8}+x=\frac{-83}{24}\)
<=> \(x=\frac{-53}{6}\)
học tốt
18 tháng 10 2015
a.1/4 +3/8 +5/16=15/16
b, 3/5 - 1/3 -1/6=1/10
c, 4/7 *5/8 *7/12=5/24
d. 25/28 : 15/24 * 6/7=60/49
PN
16 tháng 11 2015
Ta có: \(8\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)=\frac{1}{6}.48\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\)
\(=\frac{1}{6}\left(7^2-1\right)\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\)
\(=\frac{1}{6}\left(7^4-1\right)\left(7^4+1\right)\left(7^8+1\right)\)
\(=\frac{1}{6}\left(7^8-1\right)\left(7^8+1\right)\)
\(=\frac{1}{6}\left(7^{16}-1\right)\)
Vì \(7^{16}-1>\frac{1}{6}\left(7^{16}-1\right)\) nên \(7^{16}-1>8\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)\)
12 tháng 5 2022
Bài 1:
1: =-5/24+16/27+3/4
=-5/24+18/24+16/27
=13/24+16/27
=117/216+128/216=245/216
2: =-1/3+1/3+6/7=6/7
3: \(=\dfrac{1}{2}-\dfrac{7}{12}+\dfrac{1}{2}=1-\dfrac{7}{12}=\dfrac{5}{12}\)
4: \(=-\dfrac{5}{8}+\dfrac{14}{25}-\dfrac{6}{10}=\dfrac{-125+112-120}{200}=\dfrac{-133}{200}\)
2 tháng 7 2018
b, 3/5 + 4/7 + 2/8 + 10/25 + 9/21 + 28/16
= 3/5 + 4/7 + 2/8 + 2/5 + 3/7 + 14/8
= (3/5 + 2/5) + ( 4/7 + 3/7) + ( 2/8 + 14/8)
= 1 + 1 + 7/4
= 2 + 7/4 = 15/4
c , 8/7 + 7/6 + 5/8 + 10/12 + 24/28 + 6/16
= c , 8/7 + 7/6 + 5/8 + 5/6 + 6/7 + 1/2
= (8/7 + 6/7) + (7/6 + 5/6) + 5/8 + 1/2
= 14/7 + 12/6 + 5/8 + 1/2
= 2 + 2 + 5/8 + 1/2
= 4 + 9/8 = 41/8
P=24(7^2+1)(7^4+1)(7^8+1)(7^16+1)
=> 2P = 48(7^2+1)(7^4+1)(7^8+1)(7^16+1)
= (7^2 - 1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)
= (7^4 - 1)(7^4+1)(7^8+1)(7^16+1)
= (7^8 - 1)(7^8+1)(7^16+1)
= (7^16 - 1)(7^16+1)
= 7^32 - 1
=> P = (7^32 - 1) / 2