The two numbers whose arithmetic mean is 34 and their geometric mean is 16 are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 64, 4
For two numbers \(a\) and \(b\), the arithmetic mean is \(\frac{a+b}{2}\) and the geometric mean is \(\sqrt{ab}\). The two means give the sum and the product of the numbers.
Sum: \(a+b=2\times34=68\)
Product: \(ab=16^2=256\)
The numbers are the roots of \(t^2-68t+256=0\), that is, \((t-64)(t-4)=0\)
So the numbers are 64 and 4