1. Liczba b odwrotna do $a = - 4\frac{3}{5}$ $b = \frac{1}{a} = \frac{1}{- 4\frac{3}{5}} = \frac{1}{- \frac{23}{5}} = - \frac{5}{23}$

Liczba d przeciwna do $c = \frac{18}{23}$ $d = - c = - \frac{18}{23}$

Suma $b + d = - \frac{5}{23} + \left( - \frac{18}{23} \right) = - \frac{23}{23} = - 1$ a

1. $\frac{1}{2}\operatorname{}{15 - \operatorname{}\sqrt{5\ }} = \frac{1}{2}\log_{3}\left( \frac{15}{\sqrt{5}} \right) = \frac{1}{2}\log_{3}3\sqrt{5}$

$\frac{15}{\sqrt{5}} = \frac{15\sqrt{5}}{5} = 3\sqrt{5}$ b

1. |−11| + |7| = 18 $\frac{18}{2} = 9$ 7 − 9 = −2 b

2. ${k^{2} - 12m = \left( 2 - 3\sqrt{2} \right)}^{2} - 12\left( 1 - \sqrt{2} \right) = 4 - 12\sqrt{2} + 18 - 12 + 12\sqrt{2} = 10$ c

3. $a = 0,4b = > b = \frac{a}{0,4} = \frac{10a}{4} = 2,5a$ b

4. x³ + 4x ≠ 0 ∖ t x(x² + 4)≠0 x ≠ 0 ∧ x ≠ −2 ∧ x ≠ 2 d

5. −3y − mx + 12 = 0 = >3y = −mx + 12 $y = - \frac{1}{3}\text{mx} + 4$ a₁ * a₂ = −1 a

$\left( - \frac{1}{3}m \right)\left( 6 \right) = - 1$ $- \frac{1}{3}m = - \frac{1}{6}$ $m = \frac{1}{2}\text{\ \ }$

1. Ghyg

2. f(0) = a0² + b0 + c  = >c = 0 y = −ax² + bx = x(−ax+b)

3. Musi się powtórzyć (x+1) dwukrotnie i mają być też 2 różne pierwiastki a to wszystko jest w odp c

4. x² + 2x ≠ 0 x(x+2) ≠ 0 ∖ t ∖ t x ≠ 0 ∧ x ≠ −2 x = {−3,2} d

(x+3)(x²+4) = 0 x = −3 ∧ x = −2 ∧ x = 2

1. $5 = \left( - \frac{1}{3}\ m + 2 \right)0 + \frac{3}{2}m - 1$ $6 = \frac{3}{2}m$ 12 = 3m m = 4 c

2. b₁ = (−1)^2 + 3(1+2) = −1 * 2 = −2 b₂ = (−1)^4 + 3(2+1) = −1 * 3 = −3 ∖ t ∖ t S = −5 a

3. a₇ − a₅ = a₁ + 7r−(a₁ + 5r)=6 = 2r = >r = 3 a₁₀ = a₇ + 3r = 14 + 9 = 23 b