Inequality Mania

Algebra Level 5

Given a,b,c,dR a,b,c,d \in \mathbb{R} , with ab+bc+cd=8 ab+bc+cd = 8 and b2+c2=2 b^{2}+c^{2} = 2, find the minimum value of a2+d2 a^{2}+d^{2} .

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