Question

phương trình \(\left(\dfrac{3}{4}\right)^x.\sqrt{\left(\dfrac{4}{3}\right)^{\dfrac{8}{x}}}=\dfrac{9}{16}\) có 2 nghiệm x1,x2. tính S=x1+x2

Answer 1

\(\Leftrightarrow\left(\dfrac{3}{4}\right)^x.\left(\dfrac{4}{3}\right)^{\dfrac{4}{x}}=\dfrac{9}{16}\)

\(\Rightarrow\left(\dfrac{3}{4}\right)^x.\left(\dfrac{3}{4}\right)^{-\dfrac{4}{x}}=\left(\dfrac{3}{4}\right)^2\)

\(\Rightarrow\left(\dfrac{3}{4}\right)^{x-\dfrac{4}{x}}=\left(\dfrac{3}{4}\right)^2\)

\(\Rightarrow x-\dfrac{4}{x}=2\)

\(\Rightarrow x^2-2x-4=0\)

Viet: \(x_1+x_2=2\)