Question

ajutor va rog :)) ! Daca a= √21-12√3 ( 21 -12√3 totul sub primul radical ) si b = √12-6√3 ( 12 -6√3 totul sub primul radical ) , calculati media aritmetica ponderata stiind ca a are ponderea 2 si b are ponderea 4

Answer 1

se foloseste formula radicalilor compusi

a= √(21-12√3) = √(21-√432)= √[21+√(441-432)] /2-√[21-√(441-432)]/2=
=√(21+√9) /2-√(21-√9)/2=√(21+3) /2-√(21-3)/2=√12-√9=2√3-3
  
b = √(12-6√3)= √(12-√108)=√[12+√(144-108)]/2-√[12-√(144-108)]/2=
=√(12+√36)/2-√(12-√36)/2=√(12+6)/2-√(12-6)/2=√9-√3=3-√3

media aritmetica ponderata=[2(2√3-3)+4(3-√3)]/6=
  =(4√3-6+12-4√3)/6= 6/6=1