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[tex] (1+\sqrt{2} )^{2} + (1- \sqrt{2}) ^{2} [/tex] sa fie un nr natural .
Rezoilvarea sa fie detaliata !


Răspuns :

(a+b)²=a²+2ab+b², (a-b)²=a²-2ab+b²
(1+√2)²+(1-√2)²=(1²+2√2+√2²)+(1²-2√2+√2²)=(1+2√2+2)+(1-2√2+2)=1+2√2+2+1-2√2+2=6