JEE Advance - Mathematics (1984 - No. 24)
If $$a > 0,\,b > 0$$ and $$\,c > 0,$$ prove that $$\,c > 0,$$ prove that $$\left( {a + b + c} \right)\left( {{1 \over a} + {1 \over b} + {1 \over c}} \right) \ge 9$$
The statement is false.
The statement is true and can be proven using AM-GM inequality.
The statement is true and can be proven using Cauchy-Schwarz inequality.
The statement is true, but requires calculus for its proof.
The statement is true and can be proven by direct expansion and simplification.