By AM....... a+c =2b  ...so .....b =1/2 ....

and by GM.... b^4 = (a^2.c^2 )^1/2 .........

so b^2 = + ac or  -ac ......

so ac = +1/4   or - 1/4

and a+c = 1..

.so a and c are roots of quadratic equation x^2 - x + 1/4.... or x^2 - x - 1/4

and on solving a= 1/2 - 1/ 2^2