Question

Cho ba số x ; y ; z khác 0 thỏa mãn điều kiện  
Khi đó B =  có giá trị bằng 

Answer 1

Theo t/c dãy TSBN:

\(\frac{y+z-x}{x}=\frac{z+x-y}{y}=\frac{x+y-z}{z}=\frac{y+z-x+z+x-y+x+y-z}{x+y+z}=\frac{x+y+z}{x+y+z}=1\)

=> y + z - x = x => y + z = 2x 

=> z + x - y = y => z + x = 2y

=> x + y - z = z => x + y = 2z

=> \(B=\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)=\frac{y+x}{y}.\frac{z+y}{z}.\frac{x+z}{x}\)

\(=\frac{2z}{y}.\frac{2x}{z}.\frac{2y}{x}=8\)