Let the circle b x^2+y^2=r^2 having radius =r & its centre at (0,0).
(x+y)^2-2xy=r^2
Since (mi,1/mi) lies on it replacing x & y by mi & 1/mi,resp.we get
m^4-m^2r^2 +1=0
By using quadratic formula we get
mi=root[{1
root(r^4-4)}/2] Now m1,m2,m3,m4 r a permutation of these 4 values only. Multipying these 4 values we get
m1*m2*m3*m4=1
Hence proved.
Moderation Team
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