làm nhanh zùm nhak tks nhều bài nào cx đc

Question

1)Cho

$a+b+c=0$ tính

$A=[(a-b)/c + (b-c)/a + (c-a)/b)]*[(c/(a-b)+a/(b-c)+b/(c-a)]$

2)So sánh

$(10^{1979}+1)/(10^{1980}+1)$ và

$(10^{1980}+1)/(10^{1981}+1)$

score 0 · Answer 1

1. Ta có:

$\dfrac{b-c}{a}+\dfrac{c-a}{b}+\dfrac{a-b}{c}$

$=\dfrac{bc(b-c)+ac(c-a)+ab(a-b)}{abc}$

$=\dfrac{-(a-b)(b-c)(c-a)}{abc}$

$\dfrac{a}{b-c}+\dfrac{b}{c-a}+\dfrac{c}{a-b}$

$=\dfrac{a(c-a)(a-b)+b(b-c)(a-b)+c(b-c)(c-a)}{(a-b)(b-c)(c-a)}$

$=\dfrac{-(a^3+b^3+c^3)+(a+b)(b+c)(c+a)-5abc}{(a-b)(b-c)(c-a)}$

$=\dfrac{-3abc+(-c)(-a)(-b)-5abc}{(a-b)(b-c)(c-a)}$

$=\dfrac{-9abc}{(a-b)(b-c)(c-a)}$

Suy ra:

$(\dfrac{b-c}{a}+\dfrac{c-a}{b}+\dfrac{a-b}{c})(\dfrac{a}{b-c}+\dfrac{b}{c-a}+\dfrac{c}{a-b})=9$

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