Mam problem z obliczeniem dwóch wielomianów.
Zadanie brzmi: Wykonaj działania i uporządkuj otrzymany wielomian.
\(\displaystyle{ (x-5)^{2}(x- \sqrt{2})+x ^{2} (2-x \sqrt{2}) =}\)
\(\displaystyle{ (3x ^{2} -2x+5)(x-2)-(4+3x) ^{2} =}\)
Problem z dwoma wielomianami
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Hatcher
- Użytkownik
- Posty: 175
- Rejestracja: 1 maja 2008, o 15:29
- Płeć: Mężczyzna
- Lokalizacja: Polska
- Podziękował: 57 razy
- Pomógł: 14 razy
Problem z dwoma wielomianami
\(\displaystyle{ (x-5)^{2}(x- \sqrt{2})+x ^{2} (2-x \sqrt{2}) = (x-\sqrt{2})[(x-5)^2-\sqrt{2}x^2]=(x-\sqrt{2})[x^2-10x+25-\sqrt{2}x^2]=
(x-\sqrt{2})[(1-\sqrt{2})x^2-10x+25]=(1-\sqrt{2})x^3-10x^2+25x+(2-\sqrt{2})x^2+10\sqrt{2}x-25\sqrt{2}=
(1-\sqrt{2})x^3-(8+\sqrt{2})x^2+(25+10\sqrt{2})x-25\sqrt{2}}\)
\(\displaystyle{ (3x ^{2} -2x+5)(x-2)-(4+3x) ^{2} =3x^3-6x^2-2x^2+4x+5x-10-16-24x-9x^2=
3x^3-17x^2-15x-26}\)
(x-\sqrt{2})[(1-\sqrt{2})x^2-10x+25]=(1-\sqrt{2})x^3-10x^2+25x+(2-\sqrt{2})x^2+10\sqrt{2}x-25\sqrt{2}=
(1-\sqrt{2})x^3-(8+\sqrt{2})x^2+(25+10\sqrt{2})x-25\sqrt{2}}\)
\(\displaystyle{ (3x ^{2} -2x+5)(x-2)-(4+3x) ^{2} =3x^3-6x^2-2x^2+4x+5x-10-16-24x-9x^2=
3x^3-17x^2-15x-26}\)