If both a and b are positive integers greater than 1, find the smallest possible sum of a and b such that √a√a=b.

  • matematika

    Subject:

    Math
  • Author:

    hope93
  • Created:

    1 year ago

Answers 1

Answer:

(a+b) + (a-b) + (ab) + (a/b) = 36

2a + ab + a/b = 36

2ab + ab^2 + a = 36b

ab^2 + a = 36b - 2ab

a(b^2 + 1) = 2b(18 - a)

a/(18-a) = 2b/(b^2 + 1)

I tried b = 1, then a = 9

b = 2, then a = 8

b = 5, then a = 5

could not find any others.

so (9,1), (8,2), (5,5)

testing: e.g. (8,2)

8+2 + 8-2 + (8)(2) + 8/2

= 16 + 16 + 4

= 36

Step-by-step explanation:

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