Proving the Equality of Ratios: A Mathematical Analysis

[Miike012]

Homework Statement

If a/b = b/c = c/d, prove that a/d is equal to ((a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)) ^ (1/2)

The Attempt at a Solution

Prove: ((a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)) ^ (1/2) = a/d

Let: a/b = c/d = e/f = k -- Then: a = bk; c = dk; e = fk

((a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)) ^ (1/2) = (( b^5k^5 + b^2d^2k^2 + b^3d^2k^5) / (b^4dk + d^4 + bd^3k)) ^(1/2)

(Should I simplify more? (( b^5k^5 + b^2d^2k^2 + b^3d^2k^5) / (b^4dk + d^4 + bd^3k)) ^(1/2) )

= a/d = bk/d ( Because k = a/b then ((b)(a/b))/d = a/d

Once again thanks for the help.

 

[Miike012]

Nevermind... in the (( b^5k^5 + b^2d^2k^2 + b^3d^2k^5) / (b^4dk + d^4 + bd^3k)) ^(1/2) ) would I just plug in a/b or b/c or c/d for k until I get ((a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)) ^ (1/2)