21we need the value of x/y+y/z + x/z+z/x + z/y + y/x
write it as (x+y+z)(1/x+1/y + 1/z) -3
from the given equation x+ y+ z=0 so answer is -3
If x,y,z are the roots of 7x3-x-2=0, then the value of
Σ(x/y+ y/z) is _____________.
(ans= -3)
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3 Answers
21
341Another entertaining way is since x+y+z=0,
S = \sum \frac{x}{y}+\frac{y}{z} \Rightarrow S+6 = \sum \frac{x}{y}+1+\frac{y}{z}+1 = -\sum \left(\frac{z}{y} + \frac{x}{z} \right)=-S
\Rightarrow S = -3
