prosze na teraz zadanie 4 plsss.... Question from @martynaa05398

martynaa05398 @martynaa05398

April 2022 2 27 Report

prosze na teraz zadanie 4 plsss

poziomka777

Odpowiedź:

(3-√2)(√2-1)=3√2-3-2+√2=4√2-5

√3-(√3-5)(4+√3)=√3-(4√3+3-20-5√3)=√3-4√3+17+5√3=2√3+17

(√5-1)(√5+1)=5-1=4

(√3-2)(5+√2)-√6=5√3+√6-10-2√2-√6=5√3-10-2√2

Szczegółowe wyjaśnienie:

1 votes Thanks 1

basetla

$(a+b)(c+d) = ac + ad + bc + bd\\\\(a-b)(a+b) = a^{2}-b^{2}$

$a) \ (3-\sqrt{2})(\sqrt{2}-1) = 3\sqrt{2}-3-2+\sqrt{2} = 4\sqrt{2}-5\\\\\\b) \ \sqrt{3}-(\sqrt{3}-5)(4+\sqrt{3}) = \sqrt{3}-(4\sqrt{3}+3-20-5\sqrt{3})=\sqrt{3}-(-17-\sqrt{3})=\\\\=\sqrt{3}+17+\sqrt{3}=17+2\sqrt{3}$

$c) \ (\sqrt{5}-1)(\sqrt{5}+1) = (\sqrt{5})^{2}-1^{2} = 5-1 = 4\\\\\\d) \ (\sqrt{3}-2)(5+\sqrt{2})-\sqrt{6} =5\sqrt{3}+\sqrt{6}-10-2\sqrt{2}-\sqrt{6} = 5\sqrt{3}-2\sqrt{2}-10$

1 votes Thanks 1

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