Question

if a^x=b^y=c^z and b/a=c/b,prove that 2z/x+z=y/x

Answer 1

Let, a^x = b^2 = c^2 = k

a^x = k

a = k^1/x ___________(i)

b = k^1/y ___________(ii)

c = k^1/c ___________(iii)

b^2 = ac (Given)

(k^1/y)^2 = k^1/x • k^1/z

k^2/y = k^1/x+1/z

2/y = 1/x+1/z

2/y = z+x/zx

y = 2zx/z+x