Ta có M ⋮ 25 vì 75 ⋮ 25

Lại có M = 75 ( 4²⁰²¹ + 4²⁰²⁰ + ... + 4² + 4 + 1 )

= 75 . 4 ( 2²⁰²⁰ + 2²⁰¹⁹ + ... + 4 + 1 + 0,25 ) ⋮ 4 vì 4 ⋮ 4

Mà ( 25; 4 ) = 1 ⇒ M ⋮ 100

Vậy M ⋮ 100

\(M=75.4\left(4^{2020}+4^{2019}+...+4+1\right)+75+25=\)

\(=300.\left(4^{2020}+4^{2019}+...+4+1\right)+100=\)

\(=100\left[3.\left(4^{2020}+4^{2019}+...+4+1\right)+1\right]⋮100\)

\(\left(42\cdot43+43\cdot57+43\right)-360:4\)

\(=43\cdot\left(42+57+1\right)-90\)

\(=42\cdot100-90\)

=4110

\(\dfrac{x-10}{30}+\dfrac{x-14}{43}+\dfrac{x-5}{95}+\dfrac{x-148}{8}=0\\ \Rightarrow\left(\dfrac{x-10}{30}-3\right)+\left(\dfrac{x-14}{43}-2\right)+\left(\dfrac{x-5}{95}-1\right)+\left(\dfrac{x-148}{8}+6\right)=0\\ \Rightarrow\dfrac{x-100}{30}+\dfrac{x-100}{43}+\dfrac{x-100}{95}+\dfrac{x-100}{8}=0\\ \Rightarrow x-100=0\\ \Rightarrow x=100\)

\(4\left(2012-x\right)^4\ge0\\ \Rightarrow42-3\left|y-3\right|\ge0\\ \Rightarrow3\left|y-3\right|\le42\\ \Rightarrow\left|y-3\right|\le14\\ \Rightarrow-14\le y-3\le14\\ \Rightarrow-11\le y\le17\)

Vậy x=2012 và -11<=y<=17

\(M=\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}\)

\(\Rightarrow M=\left(1+\frac{1}{12}\right)+\left(1+\frac{1}{20}\right)+\left(1+\frac{1}{30}\right)+\left(1+\frac{1}{42}\right)+\left(1+\frac{1}{56}\right)+\left(1+\frac{1}{72}\right)\)

\(\Rightarrow M=6+\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)

\(\Rightarrow M=6+\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)\)

\(\Rightarrow M=6+\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)\)

\(\Rightarrow M=6+\left(\frac{1}{3}-\frac{1}{9}\right)=6+\left(\frac{3}{9}-\frac{1}{9}\right)\)

\(\Rightarrow M=6+\frac{2}{9}=\frac{54}{9}+\frac{2}{9}=\frac{56}{9}\)

( 42 x 43 + 43 x 57 + 43 ) - 360 : 4

=  43 x ( 42 + 57 + 1 ) - 90

= 43 x 100 - 90

= 4300 - 90

= 4210

Đáp án là 26269 nha

4210 nha bạn

k mik nha !