Grade Select GradeAlgebra
If a,b,c are positive, then the least value of (a+b+c)((1/a)+(1/b)+(1/c))
If a,b,c are positive, then the least value of (a+b+c)((1/a)+(1/b)+(1/c))
1 Answer
Vikas TU
Approved Tutor Answer10 Years agoon opening the brackets u will get
X=3+a/b +a/c+ b/a+b/c+c/a+c/b
on applying AM>=GM inequality on the variable part(say "y")
y>=6
on adding 3 both sides
y+3>=9
X>=9
this implies that the minimum value of the given expression is 9
X=3+a/b +a/c+ b/a+b/c+c/a+c/b
on applying AM>=GM inequality on the variable part(say "y")
y>=6
on adding 3 both sides
y+3>=9
X>=9
this implies that the minimum value of the given expression is 9
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