Prove that if $0\lt a\lt b$, then $a^2\lt \frac{1}{3}\left(a^2+ab+b^2\right)\lt b^2$.
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Lesson Parent:
Problem:
Prove that if $0\lt a\lt b$, then $a^2\lt \frac{1}{3}\left(a^2+ab+b^2\right)\lt b^2$.
Answer:
It is true that if $0\lt a\lt b$, then $a^2\lt \frac{1}{3}\left(a^2+ab+b^2\right)\lt b^2$.
