Question

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?
1. 64
2. 48
3. -32
4. 16

Answer 1

Correct Answer - Option 1 : 64

Concept used: 

For any two positive numbers AM  ≥ GM

Calculation:

Let a and b be the two numbers.

AM or Arithmetic mean = (a + b)/2

GM or Geometric mean = √(ab)

Now we will use the concept of AM  ≥ GM

⇒ (a + b)/2 ≥ √(ab)

Squaring both side

⇒ a² + b² ≥ 2ab

⇒ 97 ≥ 2ab        [Given, a² + b² = 97]

⇒ ab ≤ 97/2
⇒ ab ≤ 48.5
So, ab cannot be more than 48.5.

Among the given options, only 64 is greater than 48.5 i.e ab cannot be 64.

Hence, 64 is the correct answer.