equality

FA Thần Tốc Độ

08/02/2018 at 21:46

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For a + b + c = 0 . Prove that : \(a^3+b^3+c^3=0\)

equality

Summer Clouds moderators

16/07/2017 at 12:10

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Give \(\dfrac{a}{b}=\dfrac{a}{d}\), Prove that \(\dfrac{2a-3c}{2b-3d}=\dfrac{2a+3c}{2b+3d}\)

equality

Kayasari Ryuunosuke Coodinator 16/07/2017 at 12:47

Convert \(\dfrac{a}{b}=\dfrac{a}{d}\) to \(\dfrac{a}{b}=\dfrac{c}{d}\)

We have :

\(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow\dfrac{2a}{2b}=\dfrac{3c}{3d}\)

Apply the same sequence properties , we got :

\(\dfrac{2a}{2b}=\dfrac{3c}{3d}=\dfrac{2a-3c}{2b-3d}=\dfrac{2a+3c}{2b+3d}\)

\(\Rightarrow\dfrac{2a-3c}{2b-3d}=\dfrac{2a+3c}{2b+3d}\)
Trần Nhật Dương 16/07/2017 at 17:16

Convert $\frac{a}{b} = \frac{a}{d}$ to $\frac{a}{b} = \frac{c}{d}$

We have :

$\frac{a}{b} = \frac{c}{d} \Leftrightarrow \frac{2 a}{2 b} = \frac{3 c}{3 d}$

Apply the same sequence properties , we got :

$\frac{2 a}{2 b} = \frac{3 c}{3 d} = \frac{2 a - 3 c}{2 b - 3 d} = \frac{2 a + 3 c}{2 b + 3 d}$

$\Rightarrow \frac{2 a - 3 c}{2 b - 3 d} = \frac{2 a + 3 c}{2 b + 3 d}$
v 16/07/2017 at 12:35

\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{2a}{2b}=\dfrac{3c}{3d}=\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)