Odpowiedź:
[tex]w(x)=2x^3-x^2+3\\\\\\a)\\\\w(1-2\sqrt{3})=2\cdot(1-2\sqrt{3})^3-(1-2\sqrt{3})^2+3=\\\\=2(1^3-3\cdot1^2\cdot2\sqrt{3}+3\cdot1\cdot(2\sqrt{3})^2-(2\sqrt{3})^3)-(1^2-2\cdot1\cdot2\sqrt{3}+(2\sqrt{3})^2)+3=\\\\=2(1-3\cdot2\sqrt{3}+3\cdot4\cdot3-8\sqrt{27})-(1-4\sqrt{3}+4\cdot3)+3=\\\\=2(1-6\sqrt{3}+36-8\sqrt{9\cdot3})-(1-4\sqrt{3}+12)+3=[/tex]
[tex]=2(1-6\sqrt{3}+36-8\cdot3\sqrt{3})-1+4\sqrt{3}-12+3=2(1-6\sqrt{3}+36-24\sqrt{3})-1+4\sqrt{3}-9=\\=2(1-30\sqrt{3}+36)-1+4\sqrt{3}-9=2-60\sqrt{3}+72-1+4\sqrt{3}-9=64-56\sqrt{3}[/tex]
[tex]b)\\\\w(3\sqrt{2}+2)=2(3\sqrt{2}+2)^3-(3\sqrt{2}+2)^2+3=\\\\=2((3\sqrt{2})^3+3\cdot(3\sqrt{2})^2\cdot2+3\cdot3\sqrt{2}\cdot2^2+2^3)-((3\sqrt{2})^2+2\cdot3\sqrt{2}\cdot2+2^2)+3=\\\\=2(27\sqrt{8}+3\cdot9\cdot2\cdot2+9\sqrt{2}\cdot4+8)-(9\cdot2+12\sqrt{2}+4)+3=\\\\=2(27\sqrt{4\cdot2}+108+36\sqrt{2}+8)-(18+12\sqrt{2}+4)+3=[/tex][tex]=2(27\cdot2\sqrt{2}+116+36\sqrt{2})-(22+12\sqrt{2})+3=\\\\=2(54\sqrt{2}+116+36\sqrt{2})-22-12\sqrt{2}+3=2(90\sqrt{2}+116)-22-12\sqrt{2}+3=\\\\=180\sqrt{2}+232-22-12\sqrt{2}+3=168\sqrt{2}+213[/tex]
[tex]Zastosowane\ \ wzory\\\\(a-b)^3=a^3-3a^2b+3ab^2-b^3\\\\(a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(a+b)^2=a^2+2ab+b^2[/tex]
