**Problem:**

Let a and b be real numbers such that

.

Evaluate .

**From AMC12 2002**

Happy problem-solving! :-),

Nalin Pithwa

**Problem:**

Let a and b be real numbers such that

.

Evaluate .

**From AMC12 2002**

Happy problem-solving! :-),

Nalin Pithwa

**Question: **Consider the set .

Prove that there is a unique number such that for all .

**Solution:**

Let with . It suffices to prove that there is unique number such that

for all .

In other words, x is the minimum point of the function

, .

Hence, and .

Crisp and clear …right?

More later…

Nalin Pithwa