Question

Dane są liczby: a = 3 - 2√2 i b = 4 + 3√2. Oblicz: a-b, a*b, a/b, 1/2 a, b^2 (do kwadratu)

Answer 1

3 - 2√2 - 4 - 3√2 = -1 - 5√2

(3 - 2√2) * (4 + 3√2) = 3 * 4 + 3 * 3√2 - 2√2 * 4 - 2√2 * 3√2 = 12 + 9√2 - 8√2 - 12 = √2

(3 - 2√2) : (4 + 3√2) = (3 - 2√2)*(4 - 3√2) : (4 + 3√2)*(4 - 3√2) = (12 - 9√2 - 8√2 + 12) : 4² - (3√2)² = (24 - 17√2) : (16 -18) = (24 - 17√2): (-2)

1/2 * (3-2√2) = 3/2 - √2= 1,5 - √2

(4 + 3√2)² = 4² + 2 * 4 * 3√2 + (3√2)² = 16 + 24√2 + 18 = 34 + 24√2