Question

a/2017=b/2018=c/2019

CM

4(a-b)(b-c)=(b-c)^2

Answer 1

Sửa đề: Chứng minh: \(4\left(a-b\right)\left(b-c\right)=4\left(b-c\right)^2\)

Đặt \(\dfrac{a}{2017}=\dfrac{b}{2018}=\dfrac{b}{2019}=k\)

\(\Rightarrow\left\{{}\begin{matrix}a=2017k\\b=2018k\\c=2019k\end{matrix}\right.\)

VT: \(4\left(a-b\right)\left(b-c\right)=4\left(2017k-2018k\right)\left(2018k-2019k\right)\)

\(=4.\left(-k\right).\left(-k\right)=4k^2\) (1)

VP: \(4\left(b-c\right)^2=4\left(2018k-2019k\right)^2=4k^2\) (2)

Từ (1) và (2), suy ra:

\(4\left(a-b\right)\left(b-c\right)=4\left(b-c\right)^2\)\(\Rightarrow\) (đpcm)

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