Find value of n

Find largest possible integer n such that [\frac{na^2b^2c^2}{a^2bc+ab^2c+abc^2}]\leq (a+b)^2+(a+b+4c)^2
for all real positive a,b,c

4 Answers

62
Lokesh Verma ·

is thta the greatest integer function?

24
eureka123 ·

no..
simple bracket

11
Mani Pal Singh ·

nabca+b+c ≤ 2a2+2b2+16c2+4ab+8bc+8ac

nabc≤2a3+2b3+16c3+4a2b+20abc+8a2c+4ab2+8b2c+8bc2+8ac2

≤-nabc+2(a+b+2c)3-............................... (1)

RHS ≥ 0

Solve (1)

11
Devil ·

@ mani pal, equality never holds over here.....

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