ineq (1 Viewer)

=)(= · Jul 23, 2022

How would you prove b without am-gm

Drongoski · Jul 23, 2022

a)
$\therefore (a^2+b^2) + (b^2+c^2) + (a^2+c^2) \geq 2ab + 2bc + 2ac \\ \\ \therefore 2(a^2 + b^2 + c^2) \geq 2(ab + bc + ac )$

b)
$a^4 + b^4 = (a^2)^2 + (b^2)^2 \geq 2a^2b^2\\ \\ \therefore c^4 + d^4 \geq 2c^2d^2 \\ \\ \therefore a^4 + b^4 + c^4 + d^4 \geq 2((ab)^2 + (cd)^2) \geq 2 \times 2ab \cdot cd = 4abcd$

=)(= · Jul 23, 2022

thank you, to get 2abcd from ab^2 and cd ^2 did you use sub ab and cd into a^2 +b^2 …..

ineq (1 Viewer)

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