Question 18

# If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

Solution

Let 'a' and 'b' are those two numbers.

$$\Rightarrow$$ $$a^2+b^2 = 97$$

$$\Rightarrow$$ $$a^2+b^2-2ab = 97-2ab$$

$$\Rightarrow$$ $$(a-b)^2 = 97-2ab$$

We know that $$(a-b)^2$$ $$\geq$$ 0

$$\Rightarrow$$ 97-2ab $$\geq$$ 0

$$\Rightarrow$$ ab $$\leq$$ 48.5

Hence, ab $$\neq$$ 64. Therefore, option D is the correct answer.