Question

Dane sa liczby: a=3-2√2 i b=4+3√2.
oblicz:a-b ,a×b,a/b,1/a,b²

Answer 1

Dane są liczby: a = 3 - 2√2 i b = 4 + 3√2
a - b = 3 - 2√2 - 4 - 3√2 = -1 - 5√2
a × b = (3 - 2√2) × (4 + 3√2) = 12 + 9√2 - 8√2 - 12 = √2
a/b = 3 - 2√2 / 4 + 3√2 = (3 - 2√2)(4 - 3√2) / (4 + 3√2)(4 - 3√2) = 12 - 9√2 - 8√2 + 12 / 16 - 18 = 24 - 17√2 / - 2 = -2(- 12 + 8,5√2) / - 2 = - 12 + 8,5√2 = 8,5√2 - 12
1/a = 1/ 3 - 2√2 = 3 + 2√2 / (3 - 2√2)(3 + 2√2) = 3 + 2√2 / 9 - 8 = 3 + 2√2 / 1 = 3 + 2√2
b² = (4 + 3√2)² = 16 + 24√2 + 18 = 24√2 + 34