Question

construct x such that a/x = x/b

Answer 1

a/x=x/b
x^2=ab
x=√(ab)

CHECK:
a/x = x/b
a/√(ab) = √(ab)/b
a√(ab) / ab = √(ab)/b
√(ab) / b = √(ab)/b

YES: x=√(ab)

more like an algebra question.

Answer 2

a/x=x/b
x^2=ab
x=√(ab)