^{Problem 1 }

^{Show that positive reals such that,,
}

^{Problem 2}

Prove that the following inequalities hold for all a,b,c – sides of a triangle

**Problem 3**

Prove that for positive reals positive reals,

**Problem 4.**

Prove that for positive reals a,b,c the following inequality holds good –

**Problem 5.**

Prove that for positive reals the following inequality holds –

**Problem 6.**

Prove that for positive reals such that ,

the following inequality holds-

**Problem 7**

Prove that for positive reals with sum 2 ,

**Problem 8.**

Prove that for positive reals ,

**Problem 9.**

Let ,

Prove that ,

**Problem 10.**

Let function f be defined such that –

where a,b,c are positive reals and a,b are fixed with . Pove that the following inequality holds true –

**Problem 11.**

For positive reals with sum 1 , show that –

**Problem 12.**

For positive reals with sum 3 , show that –

**Problem 13.**

For positive reals with sum 3 , show that –

**Problem 14.**

For positive reals such that – ,

Prove that –

**Problem 15.**

For with , Prove that –

**Problem 16.**

For such that . Prove that-