CUET · MATHS · PYQ PAPER 2025
The two positive numbers whose sum is 16 and the sum of whose squares is minimum then the positive numbers are :
- A 6, 10
- B 7,9
- C 8, 8
- D 5, 11
Answer & Solution
Correct Answer
(C) 8, 8
Step-by-step Solution
Detailed explanation
Let the numbers be \(x\) and \(y\). \(x + y = 16 \implies y = 16 - x\) Minimize \(S = x^2 + y^2 = x^2 + (16 - x)^2\) \(S'(x) = 2x + 2(16 - x)(-1) = 4x - 32\) \(4x - 32 = 0 \implies x = 8\) \(y = 16 - 8 = 8\) The numbers are \(8, 8\).
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