Inequalites (1 Viewer)

[Antwan23q]

Hey, started harder 3 unit last week, and i came across this quesiton in the arnolds text book.

Show that (b+c+d)(a+c+d)(a+b+d)(a+b+c) is greater than or equal to 81abcd

My teacher explained to me Cauchy's Theorem to solve this,

(a1+a2+a3+...an)/n is greater than or equal to (a1xa2xa3x...xan)^(1/n)

sorry bout the notation, so a1 represnts a number, or letter in this case, b,
and a2 represnts c and so on.

so (b+c+d) = (b+c+d)/3 is greater than or equal to (bcd)^1/3

and then u times it by the rest of them. my teacher wasnt to sure if i could use this theorem in the hsc, if not is there any other way to solve it?

 

[KFunk]

Just use Cauchy's, it'd be a real pain otherwise.

 

[Stefano]

Just use Cauchy's, it'd be a real pain otherwise.

1. Cauchy's isn't in the syllabus.

2. It's not that much of a pain to get it out without. I don't have time to write a solution right now, but it's definetily less than 1 page and if that question were to arise then it would be worth atleast 3-4 marks, making it worth your time.

3. I will post a solution when I get the time.

 

[KFunk]

Hmm, my teacher has told me that it's fine to assume cauchy's in an HSC exam provided the question doesn't involve proving it but I geuss he could be wrong.

 

[haboozin]

any mathematically correct statement is right.