Question

Cho 4 số a, b, c, d sao cho a+b+c+d khác 0

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

Khi đó: k sẽ bằng bao nhiêu ?

Answer 1

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

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

= \(\frac{3a+3b+3c+3d}{a+b+c+d}\)

= \(\frac{3\left(a+b+c+d\right)}{a+b+c+d}\)= 3

vậy k = 3

Answer 2

b+c+d/a=c+d+a/b=d+a+b/c=a+b+c/d=k

áp dụng tc dãy tỉ số bằng nhau ta được:

b+c+d+c+d+a+d+a+b+a+b+c/a+b+c+d=k

=>3a+3b+3c+3d/a+b+c+d=k

=>3+k

=>k=3

Vậy k=3