2022 · Q44
Consider a question and two statement : Question : Is (x⁶ + y⁶)/(x⁴ + y⁴) always greater than (x⁴ + y⁴)/(x² + y²) (x ≠ y ≠ 0)?Statement - I : x > yStatement - II : x² + y² > 2xyWhich 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
Put A = x², B = y² (positive, unequal). Then (A³+B³)(A+B)-(A²+B²)² = AB(A-B)² > 0, so the first fraction is always larger. Neither statement is needed. Hence the keyed option is D.