$$2x ^{1/2}-x ^{1/4}=3$$
help

Question

myininaya · Answer

try to let u=x^1/4
then u^2=x^1/2
so you have 
2u^2-u=3
solve for u
and then solve for x

myininaya · Answer

2u^2-u-3=0
2u^2-3u+2u-3=0
u(2u-3)+(2u-3)=0
(2u-3)(u+1)=0
u=3/2
u=-1
so x^1/4=3/2
and x^1/4=-1

anonymous · Answer

This will require logarithms. If you rewrite this as 1/2 log 2x - 1/4 log x = 3, this will help. The final answer for x is x=81/16

myininaya · Answer

x=(3/2)^4=81/16
x=(-1)^4=1
we check these because we raised both sides to an even power

myininaya · Answer

we don't need logarithms

myininaya · Answer

so if we have x=1, does the equation hold?
2(1)-1=3 so 1 is not a solution
so if we have x=81/16, does the equation hold?
2(81/16)^(1/2)-(81/16)^(1/4)=2(9/4)-(3/2)=9/2-3/2=6/2=3 so x=81/16 is our only solution

anonymous · Answer

Sorry. I am taking Linear Algebra right now and it has been about 15 years since I took algebra, so I think in terms of logs when I see that. Glad you were able to figure it out. :)