Question

x=∛(7+5√2)
Sa se determine a∈Q astfel incat x=a+√2

Answer 1

[tex]x=\sqrt[3]{7+5\sqrt{2}}\\ \text{Mai intai sa observam ca:}\\ (1+\sqrt{2})^3=1+3\cdot 2+3\cdot \sqrt{2}+2\sqrt{2}=7+5\sqrt{2}\\ x=\sqrt[3]{(1+\sqrt2)^3}\\ x=1+\sqrt{2}\\ \text{Deci }a=1[/tex]