Question

IF AX=BY=CZ AND B2=AC PROVE THAT Y= 2XZ divided by XZ

Answer 1

HEY!!

ax=by=cz

b2=ac

by=cz

b=cz/y

squaring both sides

b2=c2z/y

b2=ac [given]

ac=c2z/y

a=c2z/y-1

ax=cz [given]

a=cz/x

a=c2z/y-1

cz/x=c2z/y-1

taking the exponents

z/x = 2z/y-1

z/x+1=2z/y

z+x/x=2z/y

cross multipling

[z+x]y=2zx

y=2zx/z+x

hence proved

Answer 2

hy
here is your answer
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ax=by=cz

b²=ac

by=cz

b=cz/y

squaring both sides

b²=c²z/y

b²=ac [given]

ac=c²z/y

a=c²z/y-1

ax=cz [given]

a=cz/x

a=c²z/y-1

cz/x=c²z/y-1

taking the exponents

z/x = 2z/y-1

z/x+1=2z/y

z+x/x=2z/y

cross multipling

[z+x]y=2zx

y=2zx/z+x
h.p