Đáp án:
Ta có:
`\frac{a+b+c}{d} = \frac{b+c+d}{a} = \frac{c+d+a}{b} = \frac{d+a+b}{c}`
`=> \frac{a+b+c}{d} + 1 = \frac{b+c+d}{a} + 1 = \frac{c+d+a}{b} + 1 = \frac{d+a+b}{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} `
Vì a, b, c, d khác 0 => a = b = c = d.
Ta coi `\frac{a+b+c}{d} = k.`
Lúc này `k = \frac{a+b+c}{d} = \frac{a+a+a}{a} = \frac{3a}{a} = 3.`
Vậy `\frac{a+b+c}{d} = \frac{b+c+d}{a} = \frac{c+d+a}{b} = \frac{d+a+b}{c} = 3.`
Chúc học tốt!!!