Question 13
Let $a,b,c,d$ be positive numbers such that
$$\frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2}+\frac{d^2}{1+d^2}=1.$$
The source defines $k_1$ as the maximum value of $abcd$ and $k_2$ as the minimum value of $a+b+c+d$. Which of the following is true?
The source calls $k_2$ a minimum, but its existence on the strictly positive domain must not be assumed. Assess the listed assertions on the actual domain; the solution distinguishes a minimum from an infimum.
$$\frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2}+\frac{d^2}{1+d^2}=1.$$
The source defines $k_1$ as the maximum value of $abcd$ and $k_2$ as the minimum value of $a+b+c+d$. Which of the following is true?
The source calls $k_2$ a minimum, but its existence on the strictly positive domain must not be assumed. Assess the listed assertions on the actual domain; the solution distinguishes a minimum from an infimum.