Question

Cho 2*(x+y)= 5*(y+z)= 3*(z+x)
Chứng minh: x-y/4 = y-z/5

Answer 1

2(x+y) = 5(y+z) = 3(z+x)
(x+y)/(1/2) = (y+z)/(1/5) = (z+x)/(1/3) = (x+y-z-x)/(1/2-1/3) = (z+x-y-z)/(1/3-1/5)
=> (y-z)/(1/2-1/3) = (x-y)/(1/3-1/5) => (y-z)/(1/6) = (x-y)/(2/15)
=> 6(y-z) = 15(x-y)/2 <=> 2(y-z) = 5(x-y)/2 <=> (y-z)/5 = (x-y)/4

Comments

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