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qvverty123
@qvverty123
July 2022
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Для различных ненулевых чисел a и b известно, что a^2+ab^2=a^2b+b^2. Найдите 1/a+1/b.
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MizoriesKun
a^2+ab^2=a^2b+b^2.
a^2-b^2.=a^2b-ab^2
(a -b)(a +b)= ab(a-b) разделим обе части на ab(a-b)
(a -b)(a +b) ab(a-b)
----------------- = -----------------
ab(a-b) ab(a-b)
а+b 1 1 b+a
------- =1 , заметим , что --------- + ------- = -----------
ab a b ab
1/a+1/b. =1
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Answers & Comments
a^2-b^2.=a^2b-ab^2
(a -b)(a +b)= ab(a-b) разделим обе части на ab(a-b)
(a -b)(a +b) ab(a-b)
----------------- = -----------------
ab(a-b) ab(a-b)
а+b 1 1 b+a
------- =1 , заметим , что --------- + ------- = -----------
ab a b ab
1/a+1/b. =1