JEE Advance - Mathematics (2002 - No. 19)
Suppose $$a, b, c$$ are in A.P. and $${a^2},{b^2},{c^2}$$ are in G.P. If $$a < b < c$$ and $$a + b + c = {3 \over 2},$$ then the value of $$a$$ is
$${1 \over {2\sqrt 2 }}$$
$${1 \over {2\sqrt 3 }}$$
$${1 \over 2} - {1 \over {\sqrt 3 }}$$
$${1 \over 2} - {1 \over {\sqrt 2 }}$$