Bài 1 :

\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)

\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)

\(\Rightarrow M< N\)

Bài 3 :

a) \(t^2+5t-8\) khi \(t=2\)

\(=5^2+2.5-8\)

\(=25+10-8\)

\(=27\)

b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)

\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)

\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)

c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)

\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)

\(\left(1\right)=1^3=1\)

Bài 2 :

a) \(...=2^3\left(19-14\right)+1=8.5+1=41\)

b) \(...=100-\left[60:\left(5^2-15\right)\right]=100-\left[60:10\right]=100-6=94\)

c) \(...=160:\left[17+\left(9.5-\left(14+2^3\right)\right)\right]=160:\left[17+\left(45-22\right)\right]=160:\left[17+23\right]=160:40=4\)

d) \(...=798+100\left[16-2\left(25-22\right)\right]=798+100\left[16-2.3\right]=798+100.10=798+1000=1798\)

[5 mũ 2022 cộng 2021] chia 5mũ 2021

5mũ4043chia5 mũ 2021

=5 mũ 2022

mình dag cần gâppppp

5mu2022

Đề bài hỏi chứng minh hay làm gì hả bạn?

S=5+5²+5³+...+5²⁰²⁰+5²⁰²¹

5S=5²+5³+5⁴+...+5²⁰²²

5S-S=(5+5²+5³+...+5²⁰²⁰+5²⁰²¹)-(5²+5³+5⁴+...+5²⁰²²)

4S=5-5²⁰²²

S=(5-5²⁰²²):4

  S= 5+5²+5³+...+5²⁰²⁰+5²⁰²¹

 5S=5²+5³+5⁴+...+5²⁰²¹+5²⁰²²

 5S - S=4S=5²⁰²²-5

  Ta có: 4S+5=5²⁰²²

             =4S -5 +5 =5²⁰²²

              => 4S=5²⁰²²

\(\dfrac{5^{2021}}{5^{2020}}\cdot5^2=5\cdot5^2=5^3\)

5²⁰²¹:5²⁰²⁰. 5²

= 5¹.5²

=5³

5^2021 : 5^2020 x 5^2

=  5^1 x 5^2

= 5^3

Ta có: \(A=\frac{5^{2020}+1}{5^{2020}+1}=1\)

\(B=\frac{5^{2019}+1}{5^{2020}+1}< 1\)

=> B < A

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