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If a, b, c are distinct +ve real numbers and a² + b² + c² = 1 then ab + bc + ca is

1. less than 1
2. equal to 1
3. greater than 1
4. any real no.

Correct answer: less than 1

Solution

The sum of the squares of distinct positive real numbers a, b, and c being equal to 1 implies that their pairwise products ab, bc, and ca must collectively be less than 1, as the maximum value of the products cannot exceed the total sum of their squares.

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