Ta có: (9n+3 ) chia hết cho (3n+1)

    => ( 3 . 3.n + 3.1 ) chia hết cho ( 3 n + 1)

    => 3.( 3n + 1 ) chia hết cho ( 3n +1)

    => 3 chia hết cho (3n+1)

    => 3n + 1 E Ư ( 3)

Vậy: 3n+1 = { -3;-1;1;3}

=> n = { 0} 

a/

\(2^{225}=\left(2^3\right)^{75}=8^{75}\)

\(3^{150}=\left(3^2\right)^{75}=9^{75}\)

\(8< 9\Rightarrow8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)

b/

\(12^8.9^{12}=\left(2^2\right)^8.3^8.\left(3^2\right)^{12}=2^{16}.3^{32}\)

\(18^{16}=2^{16}.\left(3^2\right)^{16}=2^{16}.3^{32}\)

\(\Rightarrow12^8.9^{12}=18^{16}\)

c/

\(45^{10}.5^{30}=\left(3^2\right)^{10}.5^{10}.5^{30}=3^{20}.5^{40}\)

\(75^{20}=3^{20}.\left(5^2\right)^{20}=3^{20}.5^{40}\)

\(\Rightarrow45^{10}.5^{30}=75^{20}\)

\(3A=3+3^2+3^3+...+3^{1000}\)

\(3A-A=3^{1000}-1\)

\(2A=3^{1000}-1\)

\(A=\frac{3^{1000}-1}{2}\)

Câu này mik cũng bít làm.

Trước tiên bạn tính 3A=3+3^2+...+3^1000

                              3A-A=3+3^2+...+3^1000-1-3-3^2-...-3^999

                              2A=3^1000-1

                               A=(3^1000-1)/2

                               Vậy.....................

cảm ơn đã ủng hộ!

\(x^2+5x-14=0\)

\(\Rightarrow x^2+7x-2x-14=0\)

\(\left(x^2+7x\right)-\left(2x+14\right)=0\)

\(x\left(x+7\right)-2\left(x+7\right)=0\)

\(\Rightarrow\left(x-2\right)\left(x+7\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-2=0\\x+7=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=2\\x=-7\end{cases}}\)

Vậy \(\orbr{\begin{cases}x=2\\x=-7\end{cases}}\)

\(x^2-5x-14=0\)

\(\Leftrightarrow\)\(x^2+2x-7x-14=0\)

\(\Leftrightarrow\)\(x\left(x+2\right)-7\left(x+2\right)=0\)

\(\Leftrightarrow\)\(\left(x-7\right)\left(x+2\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-7=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=7\\x=-2\end{cases}}}\)