Gọi \(a,b\) là hai số tự nhiên cần tìm.
Theo đề ta có: \(a:b=42\) và \(\left(a-75\right):b=37\)
- \(a:b=42\) \(\Leftrightarrow a=42b\)
- \(\left(a-75\right):b=37\) \(\Rightarrow42b-75=37b\)
\(\Leftrightarrow5b=75\) \(\Leftrightarrow b=\dfrac{75}{5}=15\)
\(\Rightarrow a=42\cdot15=630\)
Vậy hai số cần tìm là \(630\) và \(15\)

\(A=3+3^2+...+3^{101}+3^{102}\) (thêm 3³ bi sót)

\(\Rightarrow A+1=1+3+3^2+...+3^{101}+3^{102}\)

\(\Rightarrow A+1=\dfrac{3^{102+1}-1}{3-1}\)

\(\Rightarrow A+1=\dfrac{3^{103}-1}{2}\)

\(\Rightarrow A=\dfrac{3^{103}-1}{2}-1\)

\(\Rightarrow A=\dfrac{3\left(3^{102}-1\right)}{2}\)

mà \(\left(3^{102}-1\right)\) không chia hết cho 2;4;5

\(\Rightarrow A=\dfrac{3\left(3^{102}-1\right)}{2}\) không chia hết cho 2;4;5

\(\Rightarrow A\) không chia hết cho 40 \(\left(vì40=2.4.5\right)\)

\(B=4+4^2+4^3+...+4^{99}\)

\(\Rightarrow B=4\left(1+4^1+4^2\right)+4^4\left(1+4^1+4^2\right)...+4^{97}\left(1+4^1+4^2\right)\)

\(\Rightarrow B=4.21+4^4.21+...+4^{97}.21\)

\(\Rightarrow B=21\left(4+4^4+...+4^{97}\right)⋮21\)

\(\Rightarrow dpcm\)

a,x.(3\4+2\5)=1

x.20\23=1

x=1:20\23

x=20\23

b,x-9\11=0 hoặc x-25\31=0

x=9\11                x=25\31

c,x-3\7.9\14=7\3

x-2\3=7\3

x=7\3+2\3

x=9\3

x=3

a, \(\dfrac{1}{2}\) - ( - \(\dfrac{1}{3}\) ) + \(\dfrac{1}{23}\) + \(\dfrac{1}{6}\)

 =  \(\dfrac{5}{6}\)  + \(\dfrac{1}{23}\) + \(\dfrac{1}{6}\)

= 1 + \(\dfrac{1}{23}\)

 = \(\dfrac{24}{23}\) 

b, \(\dfrac{11}{24}\) - \(\dfrac{5}{41}\) + \(\dfrac{13}{24}\) + 0,5 - \(\dfrac{36}{41}\)

= (\(\dfrac{11}{24}\) + \(\dfrac{13}{24}\)) - ( \(\dfrac{5}{41}\) + \(\dfrac{36}{41}\)) + 0,5

= 1 - 1 + 0,5

= 0,5 

c,\(-\dfrac{1}{12}-\left(\dfrac{1}{6}-\dfrac{1}{4}\right)\)

=\(-\dfrac{1}{12}-\left(-\dfrac{1}{12}\right)\)

=0

d, \(\dfrac{1}{6}-\left[\dfrac{1}{6}-\left(\dfrac{1}{4}+\dfrac{9}{12}\right)\right]\)

= \(\dfrac{1}{6}-\left[\dfrac{1}{6}-1\right]\)

= \(\dfrac{1}{6}-\left(-\dfrac{5}{6}\right)\)

= 1

Rút gọn: \(\dfrac{28}{-6}=\dfrac{14}{3}\)

Quy đồng: \(-5=-\dfrac{15}{3}\)

Vì \(14>-15\) nên \(\dfrac{28}{-6}>-5\)

\(\dfrac{28}{6}=\dfrac{30-2}{6}=5-\dfrac{2}{6}=5-\dfrac{1}{3}< 5\)

\(\Rightarrow\dfrac{28}{6}< 5\Rightarrow-\dfrac{28}{6}>-5\Rightarrow\dfrac{28}{-6}>-5\)

275 = 5².11

380 = 2².5.19

780 = 2².3.5.13

2028 = 2².3.13²

3600 = 2⁴.3².5²

460 = 2².5.23

1410 = 2.3.5.47

2605 = 5.521

3420 = 2².3².5.19

720 = 2⁴.3².5

246 = 2.3.41

a) \(\left(x+4\right).\left(y-1\right)=13\)

\(x+4=13\) hoặc \(y-1=13\)

\(x=13-4\) hoặc \(y=13+1\)

Vậy \(x=9;y=14\)

b) \(xy-3x+y=20\)

\(x\left(y-3\right)+y+3=20+3\)

\(x\left(y-3\right)+\left(y-3\right)=23\)

\(\left(y-3\right).\left(x+1\right)=23\)

\(y-3=23\) hoặc \(x+1=23\)

\(y=23+3\) hoặc \(x=23-1\)

Vậy \(y=26;x=22\)

tick cho mink nhé ✔

\(C=1+5^2+5^3+5^4+...+5^{200}\)

\(\Rightarrow C+5=1+5+5^2+5^3+5^4+...+5^{200}\)

\(\Rightarrow C+5=\dfrac{5^{200+1}-1}{5-1}\)

\(\Rightarrow C+5=\dfrac{5^{201}-1}{4}\)

\(\Rightarrow C=\dfrac{5^{201}-1}{4}-5\)

\(\Rightarrow C=\dfrac{5^{201}-21}{4}\)