If a,b and c are positive real numbers such that abc=1,then the minimum value of a³+b³+c³+a²(b+c)+b²(a+c)+c²(a+b)

is

a.1

b.9a²b²c²

c.6

d.none of these

Question

If a,b and c are positive real numbers such that abc=1,then the minimum value of a 3 +b 3 +c 3 +a 2 (b+c)+b 2 (a+c)+c 2 (a+b) is a.1 b.9a 2 b 2 c 2 c.6 d.none of these

jitender lakhanpal · Answer

Dear Menka Malguri,

just check the attachement

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Ashwin Muralidharan IIT Madras · Answer

Hi Menka, Us AM-GM inequality (on the 9 terms, in the question) You will get, the minimum value of the expression to be 9. Hence Option (B). Best Regards, Ashwin (IIT Madras).

ankitesh gupta · Answer

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If a,b and c are positive real numbers such that abc=1,then the minimum value of a 3 +b 3 +c 3 +a 2 (b+c)+b 2 (a+c)+c 2 (a+b) is a.1 b.9a 2 b 2 c 2 c.6 d.none of these

If a,b and c are positive real numbers such that abc=1,then the minimum value of a³+b³+c³+a²(b+c)+b²(a+c)+c²(a+b)

is

a.1

b.9a²b²c²

c.6

d.none of these

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If a,b and c are positive real numbers such that abc=1,then the minimum value of a 3 +b 3 +c 3 +a 2 (b+c)+b 2 (a+c)+c 2 (a+b) is a.1 b.9a 2 b 2 c 2 c.6 d.none of these

If a,b and c are positive real numbers such that abc=1,then the minimum value of a3+b3+c3+a2(b+c)+b2(a+c)+c2(a+b) is a.1 b.9a2b2c2 c.6 d.none of these

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If a,b and c are positive real numbers such that abc=1,then the minimum value of a³+b³+c³+a²(b+c)+b²(a+c)+c²(a+b)

is

a.1

b.9a²b²c²

c.6

d.none of these