Odpowiedź:
Szczegółowe wyjaśnienie:
(a+b)*(a-b)= a2-b2
1) 3-2= 1
(a+b)2= a2+ 2ab+ b2
2) 5+2√10+2= 7+ 2√10
[tex]Korzystamy\ \ ze\ \ wzor\'ow\ \ skr\'oconego\ \ mno\.zenia\\\\(a-b)(a+b)=a^2-b^2\\\\(a+b)^2=a^2+2ab+b^2\\\\\\(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=(\sqrt{3})^2-(\sqrt{2})^2=3-2=1\\\\(\sqrt{5}+\sqrt{2})^2=(\sqrt{5})^2+2\cdot\sqrt{5}\cdot\sqrt{2}+(\sqrt{2})^2=5+2\sqrt{10}+2=7+2\sqrt{10}[/tex]
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Verified answer
Odpowiedź:
Szczegółowe wyjaśnienie:
(a+b)*(a-b)= a2-b2
1) 3-2= 1
(a+b)2= a2+ 2ab+ b2
2) 5+2√10+2= 7+ 2√10
[tex]Korzystamy\ \ ze\ \ wzor\'ow\ \ skr\'oconego\ \ mno\.zenia\\\\(a-b)(a+b)=a^2-b^2\\\\(a+b)^2=a^2+2ab+b^2\\\\\\(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=(\sqrt{3})^2-(\sqrt{2})^2=3-2=1\\\\(\sqrt{5}+\sqrt{2})^2=(\sqrt{5})^2+2\cdot\sqrt{5}\cdot\sqrt{2}+(\sqrt{2})^2=5+2\sqrt{10}+2=7+2\sqrt{10}[/tex]