if a^x=b^y=c^3 and b^2=ac prove that y=2xy/z+x​

Question

if a^x=b^y=c^3 and b^2=ac prove that y=2xy/z+x​

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Eloise 1 month 2021-08-17T20:33:24+00:00 2 Answers 0 views 0

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    2021-08-17T20:34:27+00:00

    Answer:

    So, y = 2xz/ (x+z) plzz follow me and I will follow you back

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    2021-08-17T20:34:47+00:00

    \huge{\mathcal{\underline{\green{ANSWER}}}}

    A^x= b^y = c^z , from this if we like to express A & c in terms of b —-

    A^x = b^y, => A = b^(y/x) , similarly , as c^z = b^y Therefore , c = b^(y/z). It is also given that ——

    b^2 = Ac,

    or,b^2 = {b^(y/x)}×{b^(y/z)} ( putting the value of A & c defined in terms of b )

    Or, b^2= b^(y/x+y/z)

    or, b^2 = b^{( yz +xy)/xz }

    or, (xy + yz)/xz =2 (as base on the both side equals (b) , power is equal)

    or, xy + yz = 2xz

    or, y(x+z) = 2xz

    So, y = 2xz/(x+z)

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