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 = ${3 \over 4},$ then the value of a is :

Question

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 = ${3 \over 4},$ then the value of a is :

${1 \over 4} - {1 \over {4\sqrt 2 }}$

${1 \over 4} - {1 \over {3\sqrt 2 }}$

${1 \over 4} - {1 \over {2\sqrt 2 }}$

${1 \over 4} - {1 \over {\sqrt 2 }}$

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