- #1
Miike012
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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.