Question

Uzasadnij, że: a) [(√2-1)(√2+1]^2=1

b) (3+√5)^1/2*(3-√5)^1/2=2

c) (2+√3)^1/2*(2-√3)^1/2=2

d) (12-√19)^1/3 (12+√19)^1/3=5

Answer 1

a)

[(√2-1)(√2+1)]^2=1

[2+√2-√2 -1]^2 =1

[ 2 -1]^2 = 1

1^2 =1

1=1

L=P

b)

(3+√5)^1/2*(3-√5)^1/2=2

[(3+√5)(3-√5)]^1/2 = 2

[(9-3√5+3√5-5)]^1/2 = 2

(9 -5)^1/2 = 2

4^1/2 = 2

2=2

L=P

c)

(2+√3)^1/2*(2-√3)^1/2=2

[(2+√3)(2-√3)] ^1/2 =2

[ 4 -2√3 +2√3- 3] ^1/2 = 2

1^1/2 = 2

1≠2

L≠P

d)

(12-√19)^1/3 (12+√19)^1/3=5

[(12-√19)(12+√19)]^1/3 = 5

(144 -19)^1/3 = 5

125^1/3 = 5

5=5

L=P