If 2^x=3^y=6^-z then 1/x+1/y+1/z=
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2x = 6 -z Þ 2 = 6-z/x -------------(i)
3y = 6 -z Þ 3 = 6-z/y -------------(ii)
Multiplying (i)and(ii)
2x3 = 6-z/x x 6-z/y
61 = 6-z/x +-z/y
Þ1 = (-z/x) +(-z/y)
Þ1= -z(1/x +1/y)
Þ1/-z = 1/x +1/y
Þ 1/x + 1/y + 1/z = 0 so do this
3y = 6 -z Þ 3 = 6-z/y -------------(ii)
Multiplying (i)and(ii)
2x3 = 6-z/x x 6-z/y
61 = 6-z/x +-z/y
Þ1 = (-z/x) +(-z/y)
Þ1= -z(1/x +1/y)
Þ1/-z = 1/x +1/y
Þ 1/x + 1/y + 1/z = 0 so do this
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