$\frac{2019a+b+c+d}{a}$ =$\frac{a+2019b+c+d}{b}$ = $\frac{a+b+2019c+d}{c}$ = $\frac{a+b+c+2019d}{d}$ Tính giá trị biểu thức M=$\frac{a+b}{c+d}$ + $\frac{b+c}{d+a}$ + $\frac{c+d}{a+b}$ + $\frac{d+a}{b+c}$
$\frac{2019a+b+c+d}{a}$ =$\frac{a+2019b+c+d}{b}$ = $\frac{a+b+2019c+d}{c}$ = $\frac{a+b+c+2019d}{d}$ Tính giá trị biểu thức M=$\frac{a+b}{c+d}$ + $\frac{b+c}{d+a}$ + $\frac{c+d}{a+b}$ + $\frac{d+a}{b+c}$
Ta có:
$\frac{2019a+b+c+d}{a}$ = $\frac{a+2019b+c+d}{b}$ = $\frac{a+b+2019c+d}{c}$ = $\frac{a+b+c+2019d}{d}$
=> $\frac{2019a+b+c+d}{a}$ – 2018 = $\frac{a+2019b+c+d}{b}$ – 2018 = $\frac{a+b+2019c+d}{c}$ – 2018 = $\frac{a+b+c+2019d}{d}$ – 2018
=> $\frac{a+b+c+d}{a}$ = $\frac{a+b+c+d}{b}$ = $\frac{a+b+c+d}{c}$ = $\frac{a+b+c+d}{d}$
+)TH1: a +b + c + d khác 0
=> a = b = c = d => M = 4
+)TH2: a + b + c + d =0
=> a + b = -(c + d) ;
b + c = -(d + a) ;
c + d = -(a + b) ;
d + a = -(b + c)
=> M = -4
Vậy M = -4 hoặc 4