GATE 2022 MA – Question 31

Find the maximum of 49−x²−y² on x+3y=10.

Show answer and explanation

Correct answer: 39 to 39

Explanation

Cauchy–Schwarz gives (x+3y)²≤(1²+3²)(x²+y²), so x²+y²≥10. Equality occurs at (x,y)=(1,3). The maximum is 49−10=**39**.

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