Matematyka

Autorzy: Anna Drążek, Ewa Duvnjak, Ewa Kokiernak-Jurkiewicz

Wydawnictwo:WSiP

Rok wydania:2013

Oblicz wartość wyrażenia 4.54 gwiazdek na podstawie 13 opinii
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a) `1/(2-sqrt(2))+3/(2+sqrt(2))=(2+sqrt(2))/((2-sqrt(2))(2+sqrt(2)))+` `(3(2-sqrt(2)))/((2+sqrt(2))(2-sqrt(2)))=` `(2+sqrt(2))/(4-2)+(3(2-sqrt(2)))/(4-2)=(2+sqrt(2))/2+(3(2-sqrt(2)))/2=`

`(2+sqrt(2)+6-3sqrt(2))/2=` `(8-2sqrt(2))/2=(2(4-sqrt(2)))/2=4-sqrt(2)`

b) `4/(3-sqrt(7))-6/(3+sqrt(7))=(4(3+sqrt(7)))/((3-sqrt(7))(3+sqrt(7)))=` `(6(3-sqrt(7)))/((3+sqrt(7))(3-sqrt(7)))=` `(12+4sqrt(7))/(9-7)-(18-6sqrt(7))/(9-7)=``(12+4sqrt(7)-18+6sqrt(7))/2=`

`=(10sqrt(7)-6)/2=(2(5sqrt(7)-3))/2=5sqrt(7)-3`

c) `2/(4+2sqrt(5))-6/(4-2sqrt(5))=(2(4-2sqrt(5)))/((4+2sqrt(5))(4-2sqrt(5)))-``(6(4+2sqrt(5)))/((4-2sqrt(5))(4+2sqrt(5)))=` `(8-4sqrt(5))/(16-4*5)-(24+12sqrt(5))/(16-20)=(8-4sqrt(5))/(-4)-` `-(24+12sqrt(5))/(-4)=(8-4sqrt(5)-24-12sqrt(5))/(-4)=` `(-16sqrt(5)-16)/(-4)=(-16(sqrt(5)+1))/(-4)=4(sqrt(5)+1)`