2
advanced-math

Find two numbers whose sum is 20 and whose product is a maximum.

A

10 and 10

B

0 and 20

C

5 and 15

D

8 and 12

Correct Answer: A

Choice A is the correct answer.

  1. Setup: Let the numbers be xx and 20−x20-x.
  2. Product Function: P(x)=x(20−x)=−x2+20xP(x) = x(20-x) = -x^2 + 20x.
  3. Maximize: Vertex x=−20/(2(−1))=10x = -20 / (2(-1)) = 10.
  4. Result: The numbers are 10 and 10. Their product is 100.

Choice B is incorrect because product is 0. Choice C is incorrect because product is 75. Choice D is incorrect because product is 96.

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Set 16: Quadratic Equations and Functions 16