Andzelikadaniluk288viz
Rozwiązane

Oblicz i uprość.
a) (2√2+2)*(2-√2)
b) (√2+1)*(1-√2)

Odpowiedź :

AstraySpirit2308viz

Cześć!

a)

[tex](2\sqrt2+2)(2-\sqrt2)=2\sqrt2\cdot2-2\sqrt2\cdot\sqrt2+2\cdot2-2\cdot\sqrt2=\\\\=4\sqrt2-2\sqrt{2^2}+4-2\sqrt2=2\sqrt2-2\cdot2+4=2\sqrt2-4+4=\boxed{2\sqrt2}[/tex]

b)

[tex](\sqrt2+1)(1-\sqrt2)=(1+\sqrt2)(1-\sqrt2)=\\\\=1^2-(\sqrt2)^2=1-2=\boxed{-1}[/tex]

АDAMiAKviz

[tex]a)=2\sqrt{2}*2-2\sqrt{2}*\sqrt{2}+2*2-2\sqrt{2}=4\sqrt{2}-4+4-2\sqrt{2}=2\sqrt{2}[/tex]

[tex]b)=(1+\sqrt{2})(1-\sqrt{2})=1-2=-1\\wzor (a-b)(a+b)=a^{2}-b^{2}[/tex]

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