CUET · MATHS · PYQ PAPER 2025
The sum of two positive numbers is 60. If the sum of their squares is minimum, then the absolute value of the difference of their cubes is
- A 0
- B 56000
- C 11500
- D 87750
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\( x + y = 60 \) \( S = x^2 + y^2 = x^2 + (60 - x)^2 = 2x^2 - 120x + 3600 \) \( \frac{dS}{dx} = 4x - 120 = 0 \) \( x = 30, y = 30 \) \( |x^3 - y^3| = |30^3 - 30^3| = 0 \)
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