Find the two positive numbers that satisfy the given requirements. - The sum of

banganX

banganX

Answered question

2021-10-09

Find the two positive numbers that satisfy the given requirements. - The sum of the first number squared and the second number is 54 and the product is a maximum.

Answer & Explanation

Bertha Stark

Bertha Stark

Skilled2021-10-10Added 96 answers

Step 1
a2+b=54
b=54a2
P=ab
P=a(54a2)
P=54aa3
dPda=543a2
dPda=0
543a2=0
3a2=54
a=32
b=54a2
b=54(32)2
b=5418=36
The sum of the first number squared and the second number is 54. Let the first and second number be a and b. The product will be P=ab. Differentiate P with respect to a and equate it to zero to get the maximum product. Substitute the value of a to the equation b=54a2 to get the value of b.
Answer 32 and 36

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