Question

1. Tính :

\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

2. Tìm x, biết :

\(5^x+5^{x+2}=650\)

3. Chứng minh:

\(5^5-5^4+5^3\)chia hết cho 7

Answer 1

2. Ta có

5^x+5^x+2=650 <=> 5^x+5^x.5²=650 <=> 5^x.(1+25)=650

<=> 5^x.26=650

<=>5^x=25=>x=2

Answer 2

3. TA CO: 5⁵-5⁴+5³

=2375⋮7

Answer 3

1.\(\dfrac{4^59^4-6^92}{2^{10}3^8+6^820}=\dfrac{\left(2^2\right)^5\left(3^2\right)^4-2^93^92}{2^{10}3^8+2^83^82^25}=\dfrac{2^{10}3^8-2^{10}3^9}{2^{10}3^8+2^{10}3^85}=\dfrac{2^{10}3^8\left(1-3\right)}{2^{10}3^8\left(1+5\right)}=\dfrac{-2}{6}=\dfrac{-1}{3}\)

2.

\(5^x+5^{x+2}=650\)

\(5^x+5^x5^2=650\)

\(5^x\left(1+25\right)=650\)

\(5^x=\dfrac{650}{1+25}=25=5^2\)

\(x=2\)

3.

\(5^5-5^4+5^3=5^3\left(5^2-5+1\right)=5^321=5^3.3.7⋮7\)