Chứng tỏ rằng: (25^25+5^49-125^16):29
Những câu hỏi liên quan
\((9^7+81^4-27^5)⋮7\)
\((25^{25}+5^{49}-125^{16})⋮29\)
\(9^7+81^4-27^5\)
\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)
\(=3^{14}+3^{16}-3^{15}\)
\(=3^{14}.\left(1+3^2-3\right)\)
\(=3^{14}.7⋮7\)
=> đpcm
\(25^{25}+5^{49}-125^{16}\)
\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)
\(=5^{50}+5^{49}-5^{48}\)
\(=5^{48}.\left(5^2+5-1\right)\)
\(=5^{48}.29⋮29\)
=> đpcm
Bài làm :
\(\text{1) }9^7+81^4-27^5\)
\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)
\(=3^{14}+3^{16}-3^{15}\)
\(=3^{14}\left(1+3^2-3\right)\)
\(=3^{14}.7⋮7\)
=> Điều phải chứng minh
\(\text{2)}25^{25}+5^{49}-125^{16}\)
\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)
\(=5^{50}+5^{49}-5^{48}\)
\(=5^{48}\left(5^2+5-1\right)\)
\(=5^{48}.29⋮29\)
=> Điều phải chứng minh
a.
\(9^7+81^4-27^5\)
\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)
\(=3^{14}+3^{16}-3^{15}\)
\(=3^{14}\left(1+3^2-3\right)\)
\(=3^{14}\left(1+9-3\right)\)
\(=3^{14}\cdot7⋮7\left(đpcm\right)\)
b.
\(25^{25}+5^{49}-125^{16}\)
\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)
\(=5^{50}+5^{49}-5^{48}\)
\(=5^{48}\left(5^2+5-1\right)\)
\(=5^{48}\left(25+5-1\right)\)
\(=5^{48}\cdot29⋮29\left(đpcm\right)\)
a.\(9^7+81^4-27^5⋮7\)
b.\(25^{25}+5^{49}_{ }-125^{16}⋮29\)
Mình đang cần đáp án gấp mọi người giúp mình nha
a) \(9^7+81^4-27^5=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)
\(=3^{14}+3^{16}-3^{15}\)
\(=3^{14}\left(1+3^2-3\right)=3^{14}\cdot7⋮7\left(đpcm\right)\)
b) \(25^{25}+5^{49}-125^{16}=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)
\(=5^{50}+5^{49}-5^{48}=5^{48}\left(5^2+5-1\right)\)
\(=5^{48}\cdot29⋮29\left(đpcm\right)\)
O BAI NAO DAY
Tính:
a) 29 - [16 + 3 . (51 - 49)]
b) 47 - [(45 . 16 - 25 . 12) : 14]
c) 100 - [60 : (125 : 25 - 3 . 5)]
d) 2345 - 1000 : [19 - 5(21 - 18)]
a) 29 - [16 + 3 . (51 - 49)]
= 29 - [ 16 + 3 . 2 ]
= 29 - [ 16 + 6 ]
= 29 - 22
= 7.
b) 47 - [(45 . 16 - 25 . 12) : 14]
= 47 - [ (720 - 300 ) : 14 ]
= 47 - [ 420 : 14 ]
= 47 - 30
= 17.
c) 100 - [60 : (125 : 25 - 3 . 5)]
= 100 - [ 60 : (5 - 3.5) ]
= 100 - [ 60 : ( 5 - 15) ]
= 100 - [60 : (-10) ]
= 100 - (-6)
= 100 + 6
= 106.
d) 2345 - 1000 : [19 - 5(21 - 18)]
= 2345 - 1000 : [ 19 - 5. 3 ]
= 2345 - 1000 : [ 19 - 15 ]
= 2345 - 1000 : 4
= 2345 - 250
= 2095
# HOK TỐT #
a)29-[16 + 3 . (51 - 49)]
=29 - [ 16 + 3 . 2]
=29 - [16 + 6 ]
=29 - 22
=7
b) 47 - [(45 . 16 - 25 . 12) : 14]
= 47 - [( 45 . 16 - 25 .12) : 14]
=47 - [(720 - 300) : 14]
=47 - [420 : 14]
=47 - 30
= 17
c) 100 - [60 : (125 : 25 - 3 . 5)]
= 100 - [ 60 : ( 5 - 15 )]
=100 - [60 : (- 10)]
= 100 - (- 6)
=94
d) 2345 - 1000 : [19 - 5(21 - 18)]
=2345 - 1000 : [ 19 -5 . 3]
=2345 - 1000 : [19 - 15]
= 2345 - 1000 : 4
=2345 - 250
=2095
TL:
a) 29 - [16 + 3 . (51 - 49)]
= 29 - ( 16+3 . 2)
= 20 - ( 16+6)
= 20 - 22
= (-2)
b) 47 - [(45 . 16 - 25 . 12) : 14]
= 47- ( 420:14)
= 47- 30
= 17
c) 100 - [60 : (125 : 25 - 3 . 5)]
= 100 - ( 60: (-10)
= 100 - (-6)
= 106
d) 2345 - 1000 : [19 - 5(21 - 18)]
= 2345 - 1000 : 4
= 2345-250
= 2095
Học tốt
Xem thêm câu trả lời
Chứng minh : 5100 -12533 - 2549 chia hết cho 29
25 mũ 25 + 5 mũ 49 - 125 mũ 16
các bạn giúp mik vs
25²⁵ + 5⁴⁹ - 125¹⁶
= (5²)²⁵ + 5⁴⁹ - (5³)¹⁶
= 5⁵⁰ + 5⁴⁹ - 5⁴⁸
= 5⁴⁸.(5² + 5 - 1)
= 5⁴⁸.24
Đúng 0
Bình luận (0)
chứng tỏ rằng: 125^7 . 25^9 . 5^20 chia hết cho 101
Chứng tỏ rằng : 5 mũ 20 + 25 mũ 11 + 125 mũ 7 chia hết cho 31.
\(=5^{20}+\left(5^2\right)^{11}+\left(5^{ }^3\right)^7\)
=\(5^{^{ }20}+5^{22}+5^{21}\)
\(=5^{20}\cdot\left(1+5^2+5^1\right)\)
=\(5^{20}\cdot\left(1+25+5\right)\)
=\(5^{20}\cdot31\)
Vì 31 chia hết chó 31 nên
\(5^{20}+25^{^{ }11}+125^7\)chia hết cho 31
Đúng 0
Bình luận (0)
\(^{5^{20}+25^{11}+125^7}\)=\(1.5^{20}+25.25^{10}+\left(5^3\right)^7\)=\(1.5^{20}+25.\left(5^2\right)^{10}+5^{21}\)=\(1.5^{20}+25.5^{20}+5.5^{20}\)
=\(^{5^{20}.\left(1+25+5\right)}\)=\(5^{20}.31\)chia hết cho 31
Vậy \(5^{20}+25^{11}+125^7\)chia hết cho 31
Đúng 0
Bình luận (0)
5^20+25^11+125^7=5^20+(5^2)^11+(5^3)^7= 5^20+5^22+5^21=5^20(1+5^2+5)=5^20.31
Vậy 5^20+25^11+125^7 chia hết cho 31
Đúng 0
Bình luận (0)
chứng tỏ rằng 125^7 + 25^9 - 5^20 chia hết cho 101
cho A = 1/4 + 1/9 + 1/16 + 1/25 +1/36 + 1/49 + 1/64 + 1/81 . Chứng tỏ A > 2/5
A=1/22+1/32+...+1/92
Ta có:1/22>1/2.3,1/32>1/3.4,...,1/92>1/9.10
⇒A>1/2.3+1/3.4+...+1/9.10
A>1/2-1/3+1/3-1/4+...+1/9-1/10
A>1/2-1/10
A>2/5(đpcm)
Đúng 1
Bình luận (0)
Ta có: A = 1/4 + 1/9 + 1/16 + 1/25 +1/36 + 1/49 + 1/64 + 1/81
Vì 1/22>1/2.3,1/32>1/3.4,...,1/92>1/9.10
=>A>1/2.3+1/3.4+...+1/9.10
=>A>1/2-1/3+1/3-1/4+...+1/9-1/10
=>A>1/2-1/10
=>A>2/5
Đúng 0
Bình luận (0)
Giải:
\(A=\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{25}+\dfrac{1}{36}+\dfrac{1}{49}+\dfrac{1}{64}+\dfrac{1}{81}\)
\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2} +\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}+\dfrac{1}{9^2}\)
Ta có:
\(\dfrac{1}{2^2}=\dfrac{1}{2.2}>\dfrac{1}{2.3}\)
\(\dfrac{1}{3^2}=\dfrac{1}{3.3}>\dfrac{1}{3.4}\)
\(\dfrac{1}{4^2}=\dfrac{1}{4.4}>\dfrac{1}{4.5}\)
\(\dfrac{1}{5^2}=\dfrac{1}{5.5}>\dfrac{1}{5.6}\)
\(\dfrac{1}{6^2}=\dfrac{1}{6.6}>\dfrac{1}{6.7}\)
\(\dfrac{1}{7^2}=\dfrac{1}{7.7}>\dfrac{1}{7.8}\)
\(\dfrac{1}{8^2}=\dfrac{1}{8.8}>\dfrac{1}{8.9}\)
\(\dfrac{1}{9^2}=\dfrac{1}{9.9}>\dfrac{1}{9.10}\)
\(\Rightarrow A>\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{10}\)
\(\Rightarrow A>\dfrac{2}{5}\left(đpcm\right)\)
Chúc bạn học tốt!
Đúng 0
Bình luận (0)