Wyznacz różnice u-w...- Zadanie 4: MATeMAtyka 2. Zakres podstawowy. Edycja 2024

Rozwiązanie

$a) u (x) - w (x) = (5 x^{9} + 2 x^{8} + 4 x^{4} + 2 x + 1) - (- 2 x^{8} - 6 x^{4} + \frac{3}{2} x - \frac{1}{2}) = 5 x^{9} + \underline{2 x^{8}} + \underline{\underline{4 x^{4}}} + \underline{\underline{\underline{2 x}}} + \underline{\underline{\underline{\underline{1}}}} + \underline{2 x^{8}} + \underline{\underline{6 x^{4}}} - \underline{\underline{\underline{\frac{3}{2} x}}} + \underline{\underline{\underline{\underline{\frac{1}{2}}}}} = 5 x^{9} + 4 x^{8} + 10 x^{4} + \frac{1}{2} x + 1 \frac{1}{2}$

$s t (u) = 9$

$s t (w) = 8$

$s t (u - w) = 9$

$b) u (x) - w (x) = (\frac{3}{4} x^{6} + \frac{1}{5} x^{4} - \frac{3}{8} x^{2} + 1) - (0, 75 x^{6} - 0, 2 x^{4} + 0, 125 x^{2}) = \underline{\frac{3}{4} x^{6}} + \underline{\underline{\frac{1}{5} x^{4}}} - \underline{\underline{\underline{\frac{3}{8} x^{2}}}} + 1 - \underline{\frac{3}{4} x^{6}} + \underline{\underline{\frac{1}{5} x^{4}}} - \underline{\underline{\underline{\frac{1}{8} x^{2}}}} = \frac{2}{5} x^{4} - \frac{1}{2} x^{2} + 1$