Question

8^\(\sqrt{x}\) – 3.4^\(\sqrt{x}\) + 2^\(\sqrt{x}\) =0 . Giải phương trình

Answer 1

Lời giải:

Đặt \(2^{\sqrt{x}}=a(a\geq 1)\)

Ta có: \(8^{\sqrt{x}}-3.4^{\sqrt{x}}+2^{\sqrt{x}}=0\)

\(\Leftrightarrow (2^{\sqrt{x}})^3-3(2^{\sqrt{x}})^2+2^{\sqrt{x}}=0\)

\(\Leftrightarrow a^3-3a^2+a=0\)

\(\Leftrightarrow a(a^2-3a+1)=0\)

\(\Rightarrow a=\frac{3+\sqrt{5}}{2}\) do $a\geq 1$

Khi đó: \(\sqrt{x}=\log_2(\frac{3+\sqrt{5}}{2})\Rightarrow x=\left(\log_2(\frac{3+\sqrt{5}}{2})\right)^2\)