GATE 2024 MA – Question 34

For positive x,y,z with xy+yz+zx=12, find maximum xyz to two decimals.

Show answer and explanation

Correct answer: 7.99 to 8.01

Explanation

AM–GM on xy,yz,zx gives $(xyz)^{2/3}\le12/3=4$, so xyz≤8. Equality requires xy=yz=zx, achieved at x=y=z=2. Maximum **8.00**.

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