RΔspuns :
2,1βQ ; 2,1011001 β R ; -2,103..βQ 1,41... βR
0,10..βQ 0,101100,...βR
xβ = 6 β Q
pentru ca 12β2 = 2Β·3Β·2β2 si 17 = 9 + 8 = 3Β² + (2β2)Β²
17 - 12β2 = 3Β² - 2 Β· 3 Β·2β2 + (2β2) Β² = binom = ( 3 - 2β2)Β²
si 17 + 12β2 = 3Β² + 2Β·3Β·2β2 + (2β2) Β² = binom = ( 3 +2β2)Β²
x β = β(3 +2β2)Β² + β( 3 - 2β2)Β²= 3 + 2β2 + 3 -2β2 = 6 β Q
xβ =
4 -2β3 = 3 +1 - 2β3 = β3Β² - 2β3 + 1Β² = binom = ( β3 -1) Β²
xβ = β11 - 4β6+ 2Β·(β3 -1) = β11 - 4β(6 +2β3 -2) = β11 -4β( 4 +2β3) =
rad. lung rad. lung
alt binom 4 + 2β3 = 3 + 2β3 +1 = β3Β² +2β3 +1Β² = ( β3 +1) Β²
= β11-4Β·(β3 +1) = β11-4β3 -4 = β7 -4β3 =
alt binom 7 - 4β3 = 4 +3 -4β3 = 2Β² - 2Β·2β3 + β3Β² = ( 2 -β3)Β²
xβ = β(2- β3)Β² = 2 - β3 β R
pentru y :
4 +2β3 =3 + 2β3 + 1 = β3 + 2Β·β3Β·1 + 1Β² = binom =( β3 +1)Β²
y = β11 + 4β6-2Β·(β3+1) = β11 + 4β(6 -2β3-2) =
rad. lund rad. lung
y= β11+4β(4-2β3)
4 -2β3 = 3 -2β3 + 1 = β3Β² - 2β3 + 1Β² = binom =(β3 -1)Β²
y = β11+4Β·(β3 -1) =β11+4β3-4 =β7 +4β3
alt binom 7 +4β3= 4 + 3 + 4β3 = 2Β² + 2Β·2β3 + β3Β² = ( 2+β3)Β²
y= β( 2 +β3)Β² = 2 + β3 β R \Q
xΒ·y = ( 2 - β3) Β·(2 + β3) = 2Β² - β3Β² = 4 - 3 = 1 β Q
xβ2 + yβ7 = ( 3β2 - 2β7) / ( 3β2 +2β7) Β·( 3β2 -2β7) =
= ( 3β2 - 2β7) / [ (3β2)Β² - (2β7)Β² ] =
= ( 3β2 - 2β7) / ( -10 )
= -3β2 /10 + 2β7 /10
daca xβ2 = - 3β2 /10 x = - 3 /10
yβ7 = 2β7 /10 y = 2/10
0,10..βQ 0,101100,...βR
xβ = 6 β Q
pentru ca 12β2 = 2Β·3Β·2β2 si 17 = 9 + 8 = 3Β² + (2β2)Β²
17 - 12β2 = 3Β² - 2 Β· 3 Β·2β2 + (2β2) Β² = binom = ( 3 - 2β2)Β²
si 17 + 12β2 = 3Β² + 2Β·3Β·2β2 + (2β2) Β² = binom = ( 3 +2β2)Β²
x β = β(3 +2β2)Β² + β( 3 - 2β2)Β²= 3 + 2β2 + 3 -2β2 = 6 β Q
xβ =
4 -2β3 = 3 +1 - 2β3 = β3Β² - 2β3 + 1Β² = binom = ( β3 -1) Β²
xβ = β11 - 4β6+ 2Β·(β3 -1) = β11 - 4β(6 +2β3 -2) = β11 -4β( 4 +2β3) =
rad. lung rad. lung
alt binom 4 + 2β3 = 3 + 2β3 +1 = β3Β² +2β3 +1Β² = ( β3 +1) Β²
= β11-4Β·(β3 +1) = β11-4β3 -4 = β7 -4β3 =
alt binom 7 - 4β3 = 4 +3 -4β3 = 2Β² - 2Β·2β3 + β3Β² = ( 2 -β3)Β²
xβ = β(2- β3)Β² = 2 - β3 β R
pentru y :
4 +2β3 =3 + 2β3 + 1 = β3 + 2Β·β3Β·1 + 1Β² = binom =( β3 +1)Β²
y = β11 + 4β6-2Β·(β3+1) = β11 + 4β(6 -2β3-2) =
rad. lund rad. lung
y= β11+4β(4-2β3)
4 -2β3 = 3 -2β3 + 1 = β3Β² - 2β3 + 1Β² = binom =(β3 -1)Β²
y = β11+4Β·(β3 -1) =β11+4β3-4 =β7 +4β3
alt binom 7 +4β3= 4 + 3 + 4β3 = 2Β² + 2Β·2β3 + β3Β² = ( 2+β3)Β²
y= β( 2 +β3)Β² = 2 + β3 β R \Q
xΒ·y = ( 2 - β3) Β·(2 + β3) = 2Β² - β3Β² = 4 - 3 = 1 β Q
xβ2 + yβ7 = ( 3β2 - 2β7) / ( 3β2 +2β7) Β·( 3β2 -2β7) =
= ( 3β2 - 2β7) / [ (3β2)Β² - (2β7)Β² ] =
= ( 3β2 - 2β7) / ( -10 )
= -3β2 /10 + 2β7 /10
daca xβ2 = - 3β2 /10 x = - 3 /10
yβ7 = 2β7 /10 y = 2/10