Question

Trebuie sa arat ca nr acesta este intreg
Ajutor.

Answer 1

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Answer 2

Trebuie sa gasim un binom in acel radical:

[tex]\sqrt{3-2\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}=\sqrt{(\sqrt{2})^2-2\cdot1\cdot\sqrt{2}+1^2}=\\\\ =\sqrt{(\sqrt{2}-1)^2}=|\sqrt{2}-1|=\sqrt{2}-1[/tex]

$a=\sqrt{2}-1-\sqrt{2}=\boxed{-1\ \in Z}$

Am mai gasit o varianta interesanta cu aceasta formula:
[tex]\sqrt{x\pm\sqrt{y}}=\sqrt{\frac{x+\sqrt{x^2-y}}{2}}\pm\sqrt{\frac{x-\sqrt{x^2-y}}{2}}\\\\ x^2\geq y[/tex]

[tex]\sqrt{3-2\sqrt{2}}=\sqrt{3-\sqrt{8}}=\sqrt{\frac{3+\sqrt{3^2-8}}{2}}-\sqrt{\frac{3-\sqrt{3^2-8}}{2}}=\sqrt{\frac{4}{2}}-\sqrt{\frac{2}{2}}=\\\\ =\sqrt{2}-1[/tex]

Si s-a ajuns la acelasi lucru.