Question

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

Answer 1

\(f\left(5-2\sqrt{3}\right)=f\left(2\right)\)

\(\Leftrightarrow\sqrt{4-2\sqrt{3}}+\left(5-2\sqrt{3}\right)m+2=\sqrt{1}+2m+2\)

\(\Leftrightarrow\sqrt{\left(\sqrt{3}-1\right)^2}+\left(5-2\sqrt{3}\right)m-2m=1\)

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

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

\(\Leftrightarrow m=\dfrac{2-\sqrt{3}}{3-2\sqrt{3}}=-\dfrac{\sqrt{3}}{3}\)