Question

1 The geometric mean of two positive integers a and b is 27 Find all possible

values of a and b

Answer 1

(a, b) ∈ {(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}

Explanation:

`√(a\cdot b)=27\\\\(√(a\cdot b))^2=27^2\\\\a\cdot b=729\\\\\\729=27\cdot27=9\cdot81=3\cdot243=1\cdot729`

So:

(a, b)∈{(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}