Найдите значение выражения (m/n-n/m)÷n-m/mn при m=√5, n=5-√5
(m/n-n/m)÷n-m/mn:
m/n-n/m =n-m /mn = 5-√5-√5 /( 5-√5)*√5 = 5-2√5 / 5√5-5
(m/n-n/m)÷n = 5-2√5 / 5√5-5 ÷ 5-√5 = 5-2√5 / √5
m/mn = √5 / ( 5-√5)*√5 = 1/ ( 5-√5)
(m/n-n/m)÷n-m/mn = 5-2√5 / √5 - 1/ ( 5-√5) = -15+7√5 / 5-√5
Ответ: -15+7√5 / 5-√5
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(m/n-n/m)÷n-m/mn:
m/n-n/m =n-m /mn = 5-√5-√5 /( 5-√5)*√5 = 5-2√5 / 5√5-5
(m/n-n/m)÷n = 5-2√5 / 5√5-5 ÷ 5-√5 = 5-2√5 / √5
m/mn = √5 / ( 5-√5)*√5 = 1/ ( 5-√5)
(m/n-n/m)÷n-m/mn = 5-2√5 / √5 - 1/ ( 5-√5) = -15+7√5 / 5-√5
Ответ: -15+7√5 / 5-√5