very hard algebra problem

[20261211]

If a:b=b:c=c:d
Prove a:d=√(a^5)+(b^2)(c^2)+(a^3)(c^2):√(b^4)c+(d^4)+(b^2)c(d^2)

 

[JeffM]

In your previous thread, you were asked to read our guidelines. Do so.

Now where have you got on this problem? Show us what you have tried or where you are stuck.

Also, do you mean

[MATH]\sqrt{a^5 + b^2c^2 + a^3c^2}.[/MATH]

 

[lookagain]

If a:b=b:c=c:d
.
.
.

You are missing grouping symbols such as parentheses, brackets, or braces:

Prove a:d = √[(a^5) + (b^2)(c^2) + (a^3)(c^2)]:√[(b^4)c + (d^4) + (b^2)c(d^2)]

Why are you working on this problem? This was at least moderately challenging
to me to finish.

 

[Dr.Peterson]

My usual way to do this is to define a:b = b:c = c:d = k, and express a, b, and c in terms of k and d. Then put these into the desired ratio, and simplify. It is not very hard this way.