Question

cho \(\frac{m}{2014}=\frac{n}{2015}=\frac{p}{2016}\)

c/m \(\left(p-m\right)^2\)= 4(m-n)(m-p)

Answer 1

Sửa đề:CM:\(\left(p-m\right)^2=4\left(m-n\right)\left(n-p\right)\)

Ta có:\(\frac{m}{2014}=\frac{n}{2015}=\frac{p}{2016}=\frac{p-m}{2016-2014}=\frac{p-m}{2}=\frac{m-n}{2014-2015}\)=

\(=\frac{m-n}{-1}=\frac{n-p}{2014-2016}=\frac{n-p}{-1}\)

\(\Rightarrow\frac{\left(p-m\right)^2}{4}=\frac{\left(m-n\right).\left(n-p\right)}{\left(-1\right).\left(-1\right)}\)

\(\Rightarrow\frac{\left(p-m\right)^2}{4}=\frac{\left(m-n\right)\left(n-p\right)}{1}\)

\(\Rightarrow\left(p-m\right)^2=4\left(m-n\right)\left(n-p\right)\)