If a, b, c are in A.P. and a², b², c² are in G.P. such that a < b < c and a + b + c = 34, then the value of a is

If a, b, c are in A.P. then a + c = 2b
Given a + b + c = 34…(1)
2b + b = 34 => b = 14
b = 14
If a², b², c² are in G.P. then (b²)² = a²c² => ac = ±116…(2)
From (1) and (2) a + 116/a = 1216
a² + 1 = 0
If 16a² + 1 = 0 => a = 14 but it is not true; because a < b
If 16a² - 1 = 0 => a = ±8/4 => a = ±2
But it is given, that a < b => a = 14 - 2√2