Quadadic Equation Substituion

[moname]

Problem: 2x ½ + x ¼ - 1 = 0

Here’s what I’ve done so far:

Determine substitution: u = x ^¼, u^2 = (x ^1/4)2 = 2x^1/2
Substitute: 2u^2 + u – 1 = 0
2 (u+1) (u-1) = 0
Identify values?: u=1, u= -1
(x 1/4) = 1, (x 1/4) = -1
(x 1/4)4 = 256
I get lost in here
somewhere ? or is this
correct and I'm not seeing?: 4?256 =

Correct Answer: 1/16 but don’t know how it’s achieved.

Thanks much for your guidance. :?

 

[Mrspi]

Problem: 2x ½ + x ¼ - 1 = 0

Here’s what I’ve done so far:

Determine substitution: u = x ^¼, u^2 = (x ^1/4)2 = 2x^1/2
Substitute: 2u^2 + u – 1 = 0<-----this is correct
2 (u+1) (u-1) = 0<----this is NOT the correct factorization
2u[sup:2ajonib7]2[/sup:2ajonib7] + u - 1 factors as (2u - 1)(u + 1)
So, either 2u - 1 = 0, which means u = 1/2, OR u + 1 = 0, which means u = -1

u = x[sup:2ajonib7]1/4[/sup:2ajonib7], so u cannot have a negative value in this problem. That leaves us with ONE solution....u = 1/2

x[sup:2ajonib7]1/4[/sup:2ajonib7] = 1/2
Raise both sides to the 4th power:

(x[sup:2ajonib7]1/4[/sup:2ajonib7])[sup:2ajonib7]4[/sup:2ajonib7] = (1/2)[sup:2ajonib7]4[/sup:2ajonib7]

NOW do you get x = 1/16?

Identify values?: u=1, u= -1
(x 1/4) = 1, (x 1/4) = -1
(x 1/4)4 = 256
I get lost in here
somewhere ? or is this
correct and I'm not seeing?: 4?256 =

Correct Answer: 1/16 but don’t know how it’s achieved.

Thanks much for your guidance. :?

 

[moname]

Thanks! At least I'm consistant in my lack of understanding. I freqently have the correct numbers for factorization but not the right order; and my negative signs are still completely wrong.

Wish there was some way to personally thank all you ladies and gents.

Have a great week

Mo

 

[Deleted member 4993]

In my opinion, x[sup:g7ed8q52]1/4[/sup:g7ed8q52] = -1 is perfectly acceptable answer.

x[sup:g7ed8q52]1/4[/sup:g7ed8q52] = -1 ? x[sup:g7ed8q52]1/2[/sup:g7ed8q52] = +1 ? x = 1