Question

Tìm m để hàm số f(x) = \(\sqrt{x+1}\) + mx + 2 (với m là tham số) thỏa mãn
\(f\left(6+4\sqrt{3}\right)\) = f(2)

Answer 1

\(f\left(6+4\sqrt{3}\right)=f\left(2\right)\)

\(\Leftrightarrow\sqrt{7+4\sqrt{3}}+\left(6+4\sqrt{3}\right)m+2=\sqrt{3}+2m+2\)

\(\Leftrightarrow\sqrt{\left(2+\sqrt{3}\right)^2}+\left(6+4\sqrt{3}\right)m-2m=\sqrt{3}\)

\(\Leftrightarrow2+\sqrt{3}+\left(4+4\sqrt{3}\right)m=\sqrt{3}\)

\(\Leftrightarrow\left(2+2\sqrt{3}\right)m=-1\)

\(\Rightarrow m=-\dfrac{1}{2+2\sqrt{3}}=\dfrac{1-\sqrt{3}}{4}\)