Question

Giúp mình câu g với ạ!

Answer 1

g) \(B=\dfrac{x^2+x+1}{x-2}=\dfrac{x^2-2x+3x-6+7}{x-2}=\dfrac{x\left(x-2\right)+3\left(x-2\right)+7}{x-2}=x+3+\dfrac{7}{x-2}=x-2+\dfrac{7}{x-2}+5\ge2\sqrt{\left(x-2\right).\dfrac{7}{x-2}}+5=2\sqrt{7}+5\)

\(B=2\sqrt{7}+5\Leftrightarrow\sqrt{x-2}=\sqrt{\dfrac{7}{x-2}}\Leftrightarrow x=2+\sqrt{7}\)

-Vậy \(B_{min}=2\sqrt{7}+5\)