JEE Main 2018 Maths Question - If a, b, c are in A.P. and a^{2},b^{2},c^{2} are in G.P. such that a

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If a, b, c are in A.P. and a^{2},b^{2},c^{2} are in G.P. such that a b c and a+ b+ c=\frac{3}{4} , then the value of a is :

Option 1) \frac{1}{4}-\frac{1}{4\sqrt{2}}
Option 2) \frac{1}{4}-\frac{1}{3\sqrt{2}}
Option 3) \frac{1}{4}-\frac{1}{2\sqrt{2}}
Option 4) \frac{1}{4}-\frac{1}{\sqrt{2}}