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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.
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