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Aflati numarul natural x , stiind ca x² = (2√2+3)² + (6-√2)² - (2√6+√5)(2√6-√5).

Răspuns :

[tex] x^{2} = 17+12 \sqrt{2} +38-12 \sqrt{2} -24+5 \\ x^{2}= 36 \\ x_{1}=6 ;x_{2}=-6[/tex]

x²=8+6√2+9+36-12√2+2-(24-2√30+2√30-5)=55-10√2-19=36-10√2