Matematyka
nikonek
2021-06-11 18:15:59
Oblicz. [latex]( sqrt{3}-4)(5+3 sqrt{3}) [/latex] [latex]( sqrt{2} +3)(3 sqrt{2}-1)[/latex] [latex]( sqrt{5}-4) ^{2} [/latex][latex](2-4 sqrt{5}) ^{2} [/latex] [latex](3+4 sqrt{3})^{2} [/latex] [latex](2 sqrt{2}-3)^{2} [/latex]
Odpowiedź
MówMiHardcor
2021-06-11 22:22:53

[latex]( sqrt{3} - 4)(5 + 3 sqrt{3}) = 5 sqrt{3} + 3 sqrt{9} - 20 - 12 sqrt{3}= 5 sqrt{3} + 9 - 20 - 12 sqrt{3} = -7 sqrt{3} - 11 [/latex] [latex]( sqrt{2} +3)(3 sqrt{2} -1)= 3 sqrt{4} - sqrt{2} + 9 sqrt{2} - 3= 6- sqrt{2} + 9 sqrt{2} - 3= 3 +8 sqrt{2} [/latex] [latex]( sqrt{5}-4)^2 (2-4 sqrt{5})^2=(21 - 8 sqrt{5})(84-16 sqrt{5})= 1764-336 sqrt{5} - 627 sqrt{5} +640= 2404 - 963 sqrt{5} [/latex] [latex](3+ 4sqrt{3})^2= (3+ 4sqrt{3})(3+ 4sqrt{3})= 9+ 12 sqrt{3}+ 12 sqrt{3} + 64=  73+24 sqrt{3} [/latex] [latex](2 sqrt{2} -3)(2 sqrt{2} -3)= 8 - 12 sqrt{2} +9= 17-12 sqrt{2} [/latex]

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