Analysis Quiz 16: Multiple-Choice Math (Square Root Inequality)
Question 1: Which of the methods below do you think can be used to prove $\sqrt{3}-\sqrt{2}\gt \sqrt{4}-\sqrt{3}$?
A. AM-GM Inequality.
B. Jensen's Inequality.
C. Cauchy–Schwarz inequality.
D. Squaring both sides of the equation and squaring again to remove the square root to make numerical comparison.
Prove $\small a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$ for all real $a,\,b,\,c\ge 0$: Second Attempt
For reals $a,\,b,\,c\ge 0$, prove the inequality
$a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$
and state when the equality holds.
$a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$
and state when the equality holds.
Prove $a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$ for all real $a,\,b,\,c\ge 0$: First Attempt
For reals $a,\,b,\,c\ge 0$, prove the inequality
$a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$
and state when the equality holds.
$a(a-c)^2+b(b-c)^2\ge (a-c)(b-c)(a+b-c)$
and state when the equality holds.
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