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If $J$ is perfect and satisfies $Z(J) = \\{0\\}$, then $\\delta$ is of the form $\\delta(x , y) = \\gamma(x \\circ y)$ for all $x , y \\in J$, where $\\gamma \\in Cent(J)$ satisfying $z \\cdot \\gamma(x \\circ y) = x \\cdot \\gamma(y \\circ z) + y \\cdot \\gamma(x \\circ z), \\forall x , y , z \\in J$. 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Let $J$ be a Jordan algebra and $\\delta :J \\times J \\rightarrow J$ a symmetric biderivation satisfying $\\delta(w , u \\circ v) = w \\cdot \\delta(u , v), \\forall u,v,w \\in J$. If $J$ is perfect and satisfies $Z(J) = \\{0\\}$, then $\\delta$ is of the form $\\delta(x , y) = \\gamma(x \\circ y)$ for all $x , y \\in J$, where $\\gamma \\in Cent(J)$ satisfying $z \\cdot \\gamma(x \\circ y) = x \\cdot \\gamma(y \\circ z) + y \\cdot \\gamma(x \\circ z), \\forall x , y , z \\in J$. 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