Odpowiedź:
d)
(11√3 - 4√7)/(√3 - √7) - (13√7 + √3)/(√12 - √28) =
= [(11√3 - 4√7)(√12 - √28) - (13√7 + √3)(√3 - √7)]/[(√3 - √7)(√12 - √28)] =
= (11√36 - 4√84 - 11√84 + 4√196 - 13√21 - 3 + 13√49 + √21) :
: (√36 - √84 - √84 + √196) =
= (11 * 6 - 15√84 + 4 * 14 - 12√21 - 3 + 13 * 7)/(6 - 2√84 + 14) =
= (66 - 15√84 + 56 - 12√21 - 3 + 91)/(20 - 2√84) =
= (210 - 15√84 - 12√21)/(20 - 2√84) =
= (210 - 15√(4 * 21) - 12√21)/(20 - 2√(4 * 21) =
= (210 - 15 * 2√21 - 12√21)/(20 - 2 * 2√21) =
= (210 - 30√21 - 12√21)/(20 - 4√21) = (210 - 42√21)/(20 - 4√21) =
= 2(105 - 21√21)/4(5 - √21) = (105 - 21√21)/2(5 - √21) =
= [(105 - 21√21)(5 + √21)]/[2(5 - √21)(5 + √21)] =
= (525 - 105√21 + 105√21 - 21 * 21)/[2(25 - 21)] =
= (525 - 441)/(2 * 4) = 84/4 = 21
