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