if-a-x-b-b-y-c-c-z-a-then-prove-that-xyz-0-

Question Number 72496 by Shamim last updated on 29/Oct/19

if a^{x} = b, b^{y} = c, c^{z} = a then prove that,

xyz = 0 .

Answered by som(math1967) last updated on 29/Oct/19

a^{x} = b \Rightarrow a^{x y} = b^{y}

a^{x y} = c \Rightarrow a^{x y z} = c^{z}

∴ a^{x y z} = a ∴ x y z = 1

s o I t h i n k i t s h o u l d b e x y z = 1

Answered by Tanmay chaudhury last updated on 29/Oct/19

a = c^{z}

a = {(b^{y})}^{z} = b^{y z}

a = {(a^{x})}^{y z} = a^{x y z} \to s o x y z = 1