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Ilyasssssss
@Ilyasssssss
July 2022
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х=1.
(a -b)(a - c)(b - c)≠0
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lenarostovnd
Verified answer
Приведем к общему знаменателю:
(a∧2(x-b)(x-c)(b-c) - b∧2(x-a)(x-c)(a-c) + c∧2(x-a)(x-b)(a-b)) / ((a-b)(a-c)(b-c)).
Возьмем только числитель и подставим x=1:
a∧2(-b)(-c)(b-c) - b∧2(-a)(-c)(a-c) + c∧2(-a)(-b)(a-b) = abc( a(b-c) - b(a-c) + c(a-b)) = abc ( ab - ac -ba+bc+ ac - bc) = abc * 0 = 0
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Answers & Comments
Verified answer
Приведем к общему знаменателю:(a∧2(x-b)(x-c)(b-c) - b∧2(x-a)(x-c)(a-c) + c∧2(x-a)(x-b)(a-b)) / ((a-b)(a-c)(b-c)).
Возьмем только числитель и подставим x=1:
a∧2(-b)(-c)(b-c) - b∧2(-a)(-c)(a-c) + c∧2(-a)(-b)(a-b) = abc( a(b-c) - b(a-c) + c(a-b)) = abc ( ab - ac -ba+bc+ ac - bc) = abc * 0 = 0