The Heronian mean H(a, b) is defined as H(a,b) = (a + sqrt(ab) + b)/3. What is the least positive integer b > 4 such that H(4, b) is also a positive integer?

Guest Oct 24, 2022

#1**+1 **

ab has to be a perfect square.

b has to be a perfect square.

(4 + sqrt(4b) + b)/3 = (4 + 2sqrt(b) + b)/3 = an integer

And from there you just plug values in.

9 doesn't work.

16 doesn't work.

25 works.

So the value of b that answers this problem is 25.

WhyamIdoingthis Oct 24, 2022