Question

Punctul b)
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Answer 1

$Avem~ de~ demonstrat~ ca: (x\circ y)\circ z=x\circ(y\circ z),\forall x,y,z\in \mathbb{R}\\\\(x\circ y)\circ z=(\sqrt[3]{x^3+y^3-1})\circ z=\sqrt[3]{(\sqrt{x^3+y^3-1})^3+z^3-1}=\\=\sqrt[3]{x^3+y^3+z^3-2}\\Pe~ de~ alta~ parte:\\x\circ (y\circ z)=x\circ (\sqrt[3]{y^3+z^3-1})=\sqrt[3]{x^3+\sqrt[3]{y^3+z^3-1}+1}=\\\sqrt[3]{x^3+y^3+z^3-2}\\Am~ obtinut~ asadar: x\circ(y\circ z)=(x\circ y)\circ z\Rightarrow lege~ asociativa.$