\(5^{61}+25^{31}+125^{21}=5^{61}+5^{62}+5^{63}\)

                                         \(=5^{61}\left(1+5+5^2\right)=5^{61}.31\)

Chia het cho 31

5^61 + 25^31 + 125^21

= 5^61 + 5^62 + 5^63

= 5^61 x (1+5+25) 

= 5^61 x 31 chia hết 31

5^61 + 25^31 + 125^21

= 5^61 + 5^62 + 5^63

= 5^61 x (1+5+25) 

= 5^61 x 31 chia hết 31

5^61+25^31+125^21 =5^61+5^62+5^63 =5^61(1+5+5^2) =5^61.31

Không chia hết cho 3 đâu bạn, chỉ 31 thôi

giải cụ thể dùng mình nhé

\(A=5^{61}+25^{31}+125^{21}\)

\(\Rightarrow A=5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(\Rightarrow A=5^{61}+5^{62}+5^{63}\)

\(\Rightarrow A=5^{61}\left(1+5+5^2\right)\)

\(\Rightarrow A=5^{61}.31⋮31\)

\(\Rightarrow A⋮31\)

Vậy \(A⋮31\)

\(A=5^{61}+25^{31}+125^{21}\)

\(A=5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(A=5^{61}+5^{62}+5^{63}\)

\(A=5^{61}\left(1+5+5^2\right)\)

\(A=5^{61}\cdot31⋮31\left(đpcm\right)\)

a ) \(5^{61}+25^{31}+125^{21}=5^{61}+5^{62}+5^{63}=5^{61}\left(1+5+25\right)=5^{61}.31⋮31\)(đpcm)

b ) \(6^3+2.6^2+3^3=2^3.3^3+2^3.3^2+3^3=3^2\left(8.3+8+3\right)=3^2.35⋮35\) (đpcm)

Vậy ........

Cảm ơn các bạn nhiều lắm nha!!!

a) Có: \(4^{51}+2^{104}+4^{53}\\ =4^{51}+\left(2^2\right)^{52}+4^{53}\\ =4^{51}+4^{52}+4^{53}\\ =4^{51}\left(1+4+4^2\right)\\ =4^{51}\cdot21⋮21\left(đpcm\right)\)

b) Có: \(125^{10}+5^{31}+25^{16}\\ =\left(5^3\right)^{10}+5^{31}+\left(5^2\right)^{16}\\ =5^{30}+5^{31}+5^{32}\\ =5^{30}\left(1+5+5^2\right)\\ =5^{30}\cdot31⋮31\left(đpcm\right)\)

c) Có: \(2^{25}+4^{13}+8^9\\ =2^{25}+\left(2^2\right)^{13}+\left(2^3\right)^9\\ =2^{25}+2^{26}+2^{27}\\ =2^{23}\left(2^2+2^3+2^4\right)\\ =2^{23}\cdot28⋮28\left(đpcm\right)\)

 5⁶¹ + 25³¹ + 125²¹ = 5⁶¹ + (5²)³¹ + (5³)²¹ = 5⁶¹ + 5⁶² + 5⁶³ = 5⁶¹ + 5⁶¹ . 5 + 5⁶¹ . 5² = 5⁶¹(1 + 5 + 5²) 

= 5⁶¹ . 31

có: 155 = 31 . 5

=> 5⁶¹ . 31 chia hết cho 31 . 5 

b) \(\left(x-\dfrac{3}{5}\right)^2=4\)

\(\Leftrightarrow\sqrt{\left(x-\dfrac{5}{3}\right)^2}=\sqrt{4}\)

\(\Leftrightarrow\left|x-\dfrac{3}{5}\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{5}=2\\x-\dfrac{3}{5}=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{5}\\x=-\dfrac{7}{5}\end{matrix}\right.\)

vậy

a) \(5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(5^{61}+5^{61}+5^{63}\)

\(5^{61}\left(1+5+5^2\right)\)

\(5^{61}.31⋮31\)

vậy....