Question

Tiìm x để 3x^2-4x+7/3x^2-4x+5 đạt GTLN

Answer 1

đK;

có \(A=\dfrac{3x^2-4x+7}{3x^2-4x+5}\)

\(=>A\)\(=\dfrac{3\left(x^2-2.\dfrac{2}{3}x+\dfrac{4}{9}+\dfrac{17}{9}\right)}{3\left(x^2-2.\dfrac{2}{3}x+\dfrac{4}{9}+\dfrac{11}{9}\right)}\)\(=\dfrac{\left(x-\dfrac{2}{3}\right)^2+\dfrac{17}{9}}{\left(x-\dfrac{2}{3}\right)^2+\dfrac{11}{9}}\)

\(=\dfrac{\left(x-\dfrac{2}{3}\right)^2+\dfrac{11}{9}+\dfrac{6}{9}}{\left(x-\dfrac{2}{3}\right)^2+\dfrac{11}{9}}=1+\dfrac{\dfrac{6}{9}}{\left(x-\dfrac{2}{3}\right)^2+\dfrac{11}{9}}\)

\(\le1+\dfrac{6}{11}=\dfrac{17}{11}\) dấu "=" xảy ra<=>x=2/3