Question

AM-GM Cauchy Schwarz Inequality for two variables

Answer 1

\[(a^2 + b^2)(c^2 + d^2) \ge (ac + bd)^2\]i thought of proving it by AM GM.

Answer 2

\[a^2c^2 + b^2 c^2 + a^2d^2 + b^2d^2 \ge a^2 c^2 + 2acbd + b^2d^2\]

Answer 3

\[b^2 c^2 + a^2 d^2 \ge 2abcd\]

Answer 4

this is an interesting scenario. hmm

Answer 5

if we let \(x_1 = b^2 c^2 \) and \(x_2 = a^2 d^2\) then\[\dfrac{b^2c^2 + a^2 d^2}{2} = \sqrt{a^2b^2c^2 d^2}\]ah, I see where this is going!

Answer 6

thanks anyway.