2022 · Q43
Consider a question and two statements : Question : Is a² + b² + c² - ab - bc - ca (a, b, c are distinct real numbers) always positive?Statement - I : a > b > cStatement - II : a + b + c = 0Which one of the following is correct in respect of the question and the statements?
Elementary MathematicsAlgebra
- AStatement - I alone is required to answer the question
- BStatement - II alone is required to answer the question
- CBoth Statement - I and Statement - II are required to answer the question
- DNeither Statement - I nor Statement - II is required to answer the question
Explanation
a²+b²+c²-ab-bc-ca = ½[(a-b)²+(b-c)²+(c-a)²], which is strictly positive for distinct real a, b, c. The answer follows with no statement at all. Hence the keyed option is D.