Let $x_1,$ $x_2,$ $x_3$ be positive real numbers such that $x_1 + 2x_2 + 3x_3 = 60.$  Find the smallest possible value of
\[x_1^2 + x_2^2 + x_3^2.\]
Question:
Let $x_1,$ $x_2,$ $x_3$ be positive real numbers such that $x_1 + 2x_2 + 3x_3 = 60.$  Find the smallest possible value of
\[x_1^2 + x_2^2 + x_3^2.\]
Answer:
Let's think step by step.

user
\frac{1800}{7}
Let $x_1,$ $x_2,$ $x_3$ be positive real numbers such that $x_1 + 2x_2 + 3x_3 = 60.$  Find the smallest possible value of
\[x_1^2 + x_2^2 + x_3^2.\]
train