Question

Bài tập: Tìm \(m\) để hàm số \(y=f\left(x\right)=\sqrt{x+1}+mx+2\) (với \(m\) là tham số) thỏa mãn \(f\left(5-2\sqrt{3}\right)=f\left(2\right)\).

Answer 1

\(f\left(5-2\sqrt{3}\right)=\sqrt{\left(5-2\sqrt{3}\right)+1}+m\left(5-2\sqrt{3}\right)+2\)
\(=\sqrt{6-2\sqrt{3}}+m\left(5-2\sqrt{3}\right)+2\)
\(f\left(2\right)=\sqrt{3}+2m+2\)
\(f\left(5-2\sqrt{3}\right)=f\left(2\right)< =>\sqrt{6-2\sqrt{3}}+m\left(5-2\sqrt{3}\right)+2=\sqrt{3}+2m+2\)
\(< =>m\left(3-2\sqrt{3}\right)=\dfrac{2\sqrt{3}-3}{\sqrt{3}+\sqrt{6-2\sqrt{3}}}< =>m=\dfrac{-1}{\sqrt{3}+\sqrt{6-2\sqrt{3}}}\)