Odpowiedź:
d)
(2√3 - 1)/(2√3+ 2) * (2√36 - 2)/(2√3 - 2) =
= [(2√3 - 1)(2√3 - 2)]/[(2√3 + 2)(2√3 - 2)] =
= (2√3 * 2√3 - 2√3 - 4√3 + 2)/[(2√3)² - 2²] =
= (4 * 3 - 6√3 + 2)/(4 * 3 - 4) = (12 - 6√3 + 2)/(12 - 4) =
= 14 - 6√3)/8 = 2(7 - 3√3)/8 = (7 - 3√3)/4
e)
√3/(√5 + √3) * (√5 - √3)/(√5 - √3) =
= √3(√5 - √3)/[(√5 + √3)(√5 - √3)] = [√(3 * 5) - (√3)²]/[(√5)² - (√3)²] =
= (√8 - 3)/(5 - 3) = (√8 - 3)/2
