How do you solve #2(x-2)^(2/3) = 50#?

1 Answer
Alan P.
Apr 10, 2015

If #2(x-2)^(2/3) = 50#
then
#(x-2)^(2/3) = 25#

If we cube both sides we get
#(x-2)^2 = 25^3 = 25^2*5^2#

or
#(x-2)^2 - 125^2 = 0#

remember that anything of the form
#(a^2-b^2)# can be factored as #(a-b)(a+b)#

we have
#((x-2)-125)((x-2)+125) = 0#
or
#(x-127)(x+123)=0#

so
#x=127#
or
#x=-123#

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