Question

Tìm số nguyên x, nếu biết

a, \(3.5^{x+2} + 4.5^{x-3}\)

b, \((\dfrac{1}{2}-\dfrac{1}{3})6^x+6^{x+2}=6^{10}+6^7\)

c, \((\dfrac{1}{3}+\dfrac{1}{6}) . 2^x + 2^{x+1}= 2^{12}+2^{10}\)

Answer 1

a/ Đề?

b/ \(\frac{1}{6}6^x+6^{x+2}=6^{10}+6^7\)

\(\Leftrightarrow6^{x-1}+6^{x+2}=6^{10}+6^7\)

\(\Leftrightarrow6^{x-1}\left(1+6^3\right)=6^7\left(1+6^3\right)\)

\(\Leftrightarrow6^{x-1}=6^7\Rightarrow x-1=7\Rightarrow x=8\)

c/ Hoàn toàn tương tự câu trên:

\(2^{x-1}+2^{x+1}=2^{12}+2^{10}\)

\(\Leftrightarrow2^{x-1}\left(1+2^2\right)=2^{10}\left(1+2^2\right)\)

\(\Leftrightarrow x=11\)