CUET · MATHS · PYQ PAPER 2025
If \(a, b, c\) are positive real numbers, then the least value of \((a+b+c)(a b+b c+c a)\) is :
- A 1
- B abc
- C 9abc
- D 3abc
Answer & Solution
Correct Answer
(C) 9abc
Step-by-step Solution
Detailed explanation
\(a+b+c \ge 3\sqrt[3]{abc}\) \(ab+bc+ca \ge 3\sqrt[3]{a^2b^2c^2} = 3(abc)^{2/3}\) \((a+b+c)(ab+bc+ca) \ge (3\sqrt[3]{abc})(3(abc)^{2/3}) = 9abc\)
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