algebra (1 Viewer)

[9876543210]

hey!
my question is

[(a+b)/2]^3 </= (a^3 + b^3)/2

thx

 

[Top Secret]

And your question is...

 

[9876543210]

i dont get why it's not coming up...
but the other half is
less or equal to (a^3 + b^3)/2

 

[Drongoski]

hey!
my question is

[(a+b)/2]^3 <!--= (a^3 + b^3)/2

thx

If you want this expanded it is:

[a³ + 3a²b + 3ab² + b³ ]/ 8

You can't be asking for this !

 

[lolokay]

i dont get why it's not coming up...
but the other half is
less or equal to (a^3 + b^3)/2

put a space between the less than sign and stuff either side

a² + b² > = 2ab
so a³ + ab² > = 2a²b
and ba² + b³ > = 2ab²
adding together gives a³ + ab² + ba² + b³ > = 2a²b + 2ab²
a³ + b³ >= a²b + ab²
(3/8)(a³ + b³)+(1/8)(a³ + b³) >= 3/8 (a²b + ab²) + 1/8 (a³ + b³)
(a³ + b³)/2 >= 1/8 (a+b)³ = ([a+b]/2)³

 

[Trebla]

 

[Aerath]

I just did RHS - LHS and proved that it's positive, therefore, hence RHS - LHS > 0, then RHS > LHS. Though it only works if a, b > 0