Question

sa se determine valoare expresiei​

Answer 1

Folosim formula de calcul prescurtat:

(a+b)³=a³+b³+3ab(a+b)

$(\sqrt[3]{\sqrt{2} +1} +\sqrt[3]{\sqrt{2} -1})^3=\sqrt{2} +1+\sqrt{2} -1+3(\sqrt[3]{\sqrt{2} +1}\cdot \sqrt[3]{\sqrt{2}-1})(\sqrt[3]{\sqrt{2} +1} +\sqrt[3]{\sqrt{2}-1} )=\\\\=2\sqrt{2} +3(\sqrt[3]{\sqrt{2} +1}\cdot \sqrt[3]{\sqrt{2}-1})(\sqrt[3]{\sqrt{2} +1} +\sqrt[3]{\sqrt{2}-1} )=2\sqrt{2} +3(\sqrt[3]{\sqrt{2} +1} +\sqrt[3]{\sqrt{2}-1} )$

$E(x)=2\sqrt{2} +3(\sqrt[3]{\sqrt{2} +1} +\sqrt[3]{\sqrt{2}-1} )-3(\sqrt[3]{\sqrt{2} +1} +\sqrt[3]{\sqrt{2}-1} )-2\sqrt{2} =0$

Un alt exercitiu gasesti aici: https://brainly.ro/tema/1023163

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