Solution of the system of equation 2x4=y4+z4,xyz=8 knowing that the logarithms logyx,logzy,logxz form a geometric progression is-
A
x=y=z=2
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B
x=y=2,z=3
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C
x=2,y=z=3
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D
x=y=z=3
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Solution
The correct option is Ax=y=z=2 ∵logyx,logzy,logxz are in G.P. ∴(logzy)2=logyxlogxz or (logzy)2=1logzy or (logzy)3=1⇒logzy=1 It is possible when y=z(x,y,z>0) from 2x4=y4+z4 2x4=2y4 x=y=z from xyz=8 x3=8 ∴x=2⇒x=y=z=2