How do you solve #(( 5x - 16) ^ { 3} - 4) ^ { 3} = 216.000#?

1 Answer
Alan P.
Aug 13, 2017

#x=color(red)((16+root(3)(10))/5)#

Explanation:

Noting that #216 = 6^3#, we have
#((5x-16)^3-4)^3=216#

#rarr (5x-16)^3-4=6#

#rarr (5x-16)^3=10#

#rarr 5x-16=root(3)(10)#

#rarr 5x=6+root(3)(10)#

#rarr x=(6+root(3)(10))/5#

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