Question

Tìm số tự nhiên n biết rằng:

a) \(\text{a}^{\text{n-5}} \).(\(\text{a}^{\text{4}} \)-3\(\text{a}^{\text{8-n}}\))=\(\text{a}^{\text{3}} \).(\(\text{a}^{\text{4}} \)-3)

b) \(\text{4}^{\text{2}}\).(3-\(\text{4}^{\text{3}}\))+27=3.(\(\text{4}^{\text{n}}\)+9)-\(\text{4}^{\text{5}}\)

Answer 1

b) \(4^2.3-4^5+27=3.4^n+27-4^5\)

\(4^2.3=3.4^n\)

=> n=2

Answer 2

a) \(a^{n-1}-3a^3=a^4-3a^3\)

\(a^{n-1}=a^4\)

=> n-1=4

=> n=5