Question 118
Positive real numbers $a$ and $b$ satisfy the following conditions: the function $f(x) = x^3 + a x^2 + 2b x - 1$ has three different real roots, while the function $g(x) = 2x^2 + 2b x + a$ does not have real roots.
Prove that $a - b \gt 1$.
Prove that $a - b \gt 1$.