Autorzy:Aleksandra Ciszkowska, Alina Przychoda, Zygmunt Łaszczyk
Wydawnictwo:WSiP
Rok wydania:2012
Oblicz (2^(4/3)+81^ (2/3))*(4³√4-18³√18+814.5 gwiazdek na podstawie 8 opinii

Oblicz (2^(4/3)+81^ (2/3))*(4³√4-18³√18+81

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`((2^(4/3)+81^(2/3))*(4root(3)4-18root(3)18+81*(9^2)^(1/3))-((-2)^(-8))^(-1/2))/(sqrt3)^(12)= `

 

 `=((2^(4/3) + (3^4)^(2/3))*(4^1*4^(1/3) - 18^1*18^(1/3)+ 9^2* 9^(2/3))-(-2)^4)/(3^(1/2))^(12)=` 

 

`=((2^(4/3)+3^(8/3))*(4^(1 1/3)- 18^(1 1/3)+ 9^(2 2/3))-2^4)/(3^6)=` `((2^(4/3)+3^(8/3))*((2^2)^(1 1/3)- (2*9)^(1 1/3)+(3^2)^(2 2/3))-2^4)/(3^6)=` 

`=((2^(4/3)+3^(8/3))*(2^(2 2/3)- (2^ (1 1/3)*9^(1 1/3))+3^(4 4/3))-2^4)/(3^6)` `=((2^(4/3)+3^(8/3))*(2^(2 2/3)-2^(1 1/3)*(3^2)^(1 1/3)+ 3^(5 1/3))-2^4)/3^6=`         

`=((2^(4/3)+3^(8/3))*(2^(2 2/3)-2^(1 1/3)*3^(2 2/3)+ 3^(5 1/3))-2^4)/(3^6)=` 

`=((2^(4/3)+3^(8/3))*(2^(8/3)-2^(1 1/3)*3^(2 2/3)+ 3^(16/3))-2^4)/(3^6)=`

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

Korzystamy ze wzoru skróconego mnożenia:

`_((a+b)(a^2-ab+b^2)=a^3+b^3)`

 

`=((2^(4/strike3))^strike3+(3^(8/strike3))^strike3-2^4)/3^6=(2^4+3^8-2^4)/3^6=3^8/3^6=3^2=9`