Question

Cho a/2014=b/2015=c/2016. CMR: 4(a-b)(b-c)=(c-a)²

Answer 1

Dat \(\frac{a}{2014}=\frac{b}{2015}=\frac{c}{2016}=k\)

---> a = 2014k, b=2015k , c=2016k

VE trai : 4. ( 2014k-2015k). (2015k-2016k)=4. (-1k).(-1k)=4k²

Ve phai: (2016k-2014k)²=(2k)²=4k²

---> ve trai = ve phai----> dpcm

Answer 2

Ta có

 \(\frac{a}{2014}=\frac{b}{2015}=\frac{c}{2016}=\frac{a-b}{-1}=\frac{b-c}{-1}=\frac{c-a}{2}\)

Suy ra

\(\left(\frac{a-b}{-1}\right)\left(\frac{b-c}{-1}\right)=\left(\frac{c-a}{2}\right)^2\)

-->\(\left(a-b\right)\left(b-c\right)=\left(c-a\right)^2\cdot2^2\)

-->\(\left(a-b\right)\left(b-c\right)=\left(c-a\right)^2\cdot4\)

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

Answer 3

Nguyễn Thái Thuận Nguyên sai rùi. 

(a-b)(b-c)=(c-a)².4

=> [(a-b)(b-c)]/4=(c-a)^2

Answer 4

a/2014=b/2015=c/2016

suy ra a-b/-1=b-c/-1=c-a/2

suy ra c-a=-2(a-b)=-2(b-c)         

suy ra (c-a)^2=-2(a-b).-2(b-c)=4(a-b)(b-c)                                   

Answer 5

easy game