Question

cho dãy tỉ số = nhau :2a+b+c+d/a=a+2b+c+b/b=a+b+2c+d/c=a+b+c+2d/d

tìm giá chị biểu thức:m= a+b/c+d + b+c/d+a + c+d/a+b + d+a/b+c

giúp mik với!!!!!!!!!!

cám ơn bn đã giúp mik nha!!!!!

Answer 1

Ta có \(\frac{2a+b+c+d}{a}=\frac{a+2b+c+d}{b}=\frac{a+b+2c+d}{c}=\frac{a+b+c+2d}{d}\)

=> \(1+\frac{a+b+c+d}{a}=1+\frac{a+b+c+d}{b}=1+\frac{a+b+c+d}{c}=1+\frac{a+b+c+d}{d}\)

=> \(\frac{a+b+c+d}{a}=\frac{a+b+c+d}{b}=\frac{a+b+c+d}{c}=\frac{a+b+c+d}{d}\)

Khi a + b + c + d => a + b = -(c + d) ; 

b + c = -(a + d) ; 

c + d = -(a + b) 

d + a = -(b + c)

Khi đó \(M=\frac{-\left(c+d\right)}{c+d}+\frac{-\left(a+d\right)}{a+d}+\frac{-\left(a+b\right)}{a+b}+\frac{-\left(b+c\right)}{b+c}\)

= (-1) + (-1) + (-1) + (-1) = -4

Khi a + b + c + d \(\ne0\)

=> \(\frac{1}{a}=\frac{1}{b}=\frac{1}{c}=\frac{1}{d}\Rightarrow a=b=c=d\)

Khi đó M = \(\frac{2a}{2a}+\frac{2b}{2b}+\frac{2c}{2c}+\frac{2d}{2d}=2+2+2+2=8\)

Vậy khi a + b + c + d = 0 thì M = -4

khi a + b + c + d \(\ne\)0 thì M = 8

Answer 2

thanks bn nha!!!!!!!!!!!!