# Cho 1/c=1/2 (1/a+1/b) ( vs a,b,c ≠0, b≠c). CMR a/b=a-c/c-b Giúp mk vs, hết điểm r

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Cho 1/c=1/2 (1/a+1/b) ( vs a,b,c ≠0, b≠c). CMR a/b=a-c/c-b
Giúp mk vs, hết điểm r

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1. thanhmai

1/c=1/2(1/a+1/b)

⇒2/c=1/a+1/b=(a+b)/(ab)

⇒2ab=(a+b)c=ac+bc

⇒ab-ac=bc-ab

⇒a(b-c)=b(c-a)

⇒a/b=(c-a)/(b-c)=(a-c)/(c-b)

Trả lời
2. truongankim

$\dfrac1c =\dfrac12\left(\dfrac1a +\dfrac1b\right)$

$\to \dfrac1c =\dfrac{a+b}{2ab}$

$\to 2ab = c(a+b)$

$\to ab – ac = bc – ab$

$\to a(b-c) = b(c-a)$

$\to \dfrac ab =\dfrac{c-a}{b-c}$

$\to \dfrac ab =\dfrac{a – c}{c -b}$ (đpcm)

Trả lời
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