Question
Question: If a, b and c are distinct positive numbers, then expression (b + c – a) (c + a – b) (a + b – c) – ...
If a, b and c are distinct positive numbers, then expression
(b + c – a) (c + a – b) (a + b – c) – abc is:
A
Positive
B
Negative
C
Non-positive
D
Non-negative
Answer
Non-positive
Explanation
Solution
a2 ³ a2 – (b – c)2, b2 ³ b2 – (a – c)2
and c2 ³ c2 – (a – b)2
Ž a2b2c2 ³ (b + c –a)2 (c + a – b)2 (a + b – c)2
Ž abc ³ (b + c – a) (c + a – b) (a + b – c)
Hence given expression is non-positive.
Ž choice (3) is correct.