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5^6+5^7+5^8
=5^6.(1+5+5^2)
=5^6.31 chia hết cho 31
7^6+7^5-7^4
=7^4.(7^2+7-1)
=7^4.55 chia hết cho 11
BÀI 2:
a) \(5^6+5^7+5^8=5^6\left(1+5+5^2\right)=5^6.31\) \(⋮\)\(31\)
b) \(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.55\)\(⋮\)\(11\)
c) \(2^3+2^4+2^5=2^3.\left(1+2+2^2\right)=2^3.7\)\(⋮\)\(7\)
d) mk chỉnh đề
\(1+2+2^2+2^3+...+2^{59}\)
\(=\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{58}+2^{59}\right)\)
\(=\left(1+2\right)+2^2\left(1+2\right)+...+2^{58}\left(1+2\right)\)
\(=\left(1+2\right)\left(1+2^2+...+2^{58}\right)\)
\(=3\left(1+2^2+...+2^{58}\right)\)\(⋮\)\(3\)
Ta có :
1/22 < 1/1.2 = 1/1 - 1/2
1/32 < 1/2.3 = 1/2 - 1/3
..........
1/1002 < 1/99.100 = 1/99 - 1/100
=> 1/22+1/32+1/42+......+1/1002 < 1/1 - 1/2 + 1/2 - 1/3 + .... + 1/99 - 1/100 = 1 - 1/100 < 1
=> 1/22+1/32+1/42+......+1/1002 < 1 ( dpcm )
A=2x(1+2)+23x(1+2)+...+259x(1+2)
=2x3+23x3+...+259x3
=3x(2+23+...+259) chia hết cho 3
vậy A chia hết cho 3
a) \(63^7< 64^7=\left(2^6\right)^7=2^{42}< 2^{48}=\left(2^4\right)^{12}=16^{12}\Rightarrow63^7< 16^{12}\)
b) \(3^{151}>3^{150}=\left(3^2\right)^{75}=9^{75}>8^{75}=\left(2^3\right)^{75}=2^{225}\)
c) \(9^{20}=\left(3^2\right)^{20}=3^{40}>3^{39}=\left(3^3\right)^{13}=27^{13}\Rightarrow9^{20}>27^{13}\)
bài 2:
a)\(2^x=32\Leftrightarrow2^x=2^5\Leftrightarrow x=5\)
b)\(2x+3^4=7^2\Leftrightarrow2x+81=49\Leftrightarrow2x=-32\Leftrightarrow x=-16\)
c)\(12x-33=3^2\Leftrightarrow12x-33=9\Leftrightarrow12x=42\Leftrightarrow x=\frac{7}{2}\)
1 dm2 50 cm2
4 m2 23 dm2
7 cm2 9mm2
20 dam2 10 m2
45 hm2 67 dam2 40,9 cm2
80 dam2 700 m2
chúc bạn học tốt
Ta có : B = x3 + x2y -xy2 -y3 +x2 -y2 + 2x + 2y + 3
= x2 (x+y+1)-y2(x + y + 1)+2(x+y+1) +2
= x2 . 0 - y2 . 0 + 2. 0 + 2
= 2
ta có B=x^2(x+y)-y^2(x+y)+x^2-y^2+2(x+y)+3
=)B=x^2(x+y)+x^2-y^2(x+y)-y^2+2(x+y)+2+1
=)B=x^2(x+y+1)-y^2(x+y+1)+2(x+y+1)+1
=)B=0-0+0+1=1