Question

If a^x=B^y=c^z=d^w prove that x+y\xy=z+w/zw

Answer 1

to satisfy the given eq x=y=z=w
x+y/xy=z+w/zw
1=1 hence proved

Answer 2

Step-by-step explanation:

Correction:

If a^x = b^y = c^z = d^w and ab = cd, prove that (x+y)/xy = (z+w)/zw

Given:

a^x = b^y = c^z = d^w and ab = cd

To prove:

(x+y)/xy = (z+w)/zw

Solution:

Let a^x = b^y = c^z = d^w = k.

⇒a = (k)^1/x, b = (k)^1/y, c = (k)^1/z and d = (k)^1/w

since, ab = cd

∴ (k)^1/x × (k)^1/y = (k)^1/z × (k)^1/w

⇒k^[(1/x) + (1/y)] = k^[(1/z) + (1/w)]

⇒ k^[(y+x)/xy] = k^[(w+z)/wz]

Hence, (x + y)/xy = (z + w)/wz