Zad. 1
Mając dane x=√3-2√5
y=4+5√3
wyznacz:
x+y=√3-2√5 + 4+5√3=
x-y=√3-2√5 - 4+5√3=
x×y=(√3-2√5)(4+5√3)=

x/y √3-2√5
=...........=
4+5√3

x²=(√3-2√5)²

zad 2 usun niewymierność z mianownika

a) 2√3+6 ( 3+6 jest pod pierwiastkiem )
-------- =
4√3

b) 3-√5
------- =
2+3√5

zad. 3 oblicz
a) ( ¼⁵) × 16 ÷ ( ¹/⁶√₈) =
b) ( 32 )⁻⁴ × ( 1/64 )⁻⁴=
c) ( 0,25 ²) × ( ⅛) × √32 =
Proszę z obliczeniami.

1

Odpowiedzi

2012-08-05T14:04:57+02:00

Zad.1

x = √3-2√5

y = 4+5√3

 

x+y = √3-2√5 + 4+5√3 = √3+5√3-2√5+4 = 6√3-2√5+4

 

x-y = √3-2√5 -(4+5√3 = √3-2√5-4-5√3 = -4√3-2√5-4

 

x *y = (√3-2√5)(4+5√3) = 4√3+15-8√5-10√15 = 4√3-8√4-10√15+15

 

x/y = (√3-2√5)/(4+5√3) * (4-5√3)/(4-5√3) = (4√3-8√5-15+10√15)/(4-15) =

      = -(4√3-8√5+10√15-15)/11 = (15-10√15+8√5+4√3)/11

 

x² = (√3-2√5)² = √3²-2*√3 * 2√5 +(2√5)² = 3-4√15+20 = 23-4√15

 

Zad.2

a)

2√(3+6)/4√3 * √3/√3 = 2√9 * √3/12 = 2*3*√3/12 = 6√3/12 = √3/2

b)

(3-√5)/2+3√5) * (2-3√5)/(2-3√5) = (6-9√5-2√5 +15)/(4-15) = (-21+11√5)/11 = √5-21/11

c)

   (0,25)² *(1/8) * √32 =  

= (25/100)² *(1/8) *√(16*2) =

= (1/4)² *(1/8) * 4 * √2 =

= 1/16 * 1/8 * 4√2 =

= 1/4 * 1/8 *√2 =

= (1/32)√2 = 0,0312√2