How do i solve #2(x-1)^(1/4)=(6x-14)^(1/4)#? (The 1/4 are fractions raised, im not trying to divide, sorry for missunderstanding)

1 Answer
Hriman
Mar 29, 2018

#"No real solution"#
#x=1/5# for a complex solution

Explanation:

#2(x-1)^(1/4)= (6x-14)^(1/4)#

  1. Raise both sides to the fourth power
    #(2(x-1)^(1/4))^4= ((6x-14)^(1/4))^4#

  2. Simplify
    #2^4*(x-1)^(1/4*4)= (6x-14)^(1/4*4)#
    #16(x-1)= (6x-14)#

  3. Distribute
    #16x-16= 6x-14#

  4. Solve for x
    #10x=2#
    #x=1/5#

  5. Check if the solution is real
    #2(1/5-1)^(1/4)= (6(1/5)-14)^(1/4)#
    #2(-4/5)^(1/4)= (6/5-70/5)^(1/4)#
    #2(-4/5)^(1/4)= (-64/5)^(1/4)#
    Fourth root of negative numbers will yield a complex number with an imaginary part to it
    #"No real solutions"#

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