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If x + y + z = 13, then the maximum value of (x - 2 )(y + 1)(z - 3) is

A) 25
B) 30
C) 54
D) 27

Correct Answer:




D) 27

Description for Correct answer:
We know that, AM greater than equal to GM

\( \large\frac{(x - 2) + (y + 1) + (z - 3)}{3} \ge \sqrt[3]{(x - 2)(y + 1)(z - 3)} \)

= > \( \large\frac{13 - 4}{3} \ge \sqrt[3]{(x - 2)(y + 1)(z -3)} \)

= > \( \large 3 \ge \sqrt[3]{(x - 2)(y + 1)(z - 3)} \)

= >\( \large 27 \ge (x - 2)(y + 1)(z - 3) \)

Thus , maximum value of (x - 2)(y + 1)(z - 3) is 27.

Part of solved Average questions and answers : >> Aptitude >> Average

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