# Thread: Need help with a specific method in reducing quadratic equations

1. ## Need help with a specific method in reducing quadratic equations

Ok, so theoretically some equations can be treated as quadratic and we're supposed to solve by having u=b (the middle term) and multiply the middle term, and 'a,' by u.

For example......

x-[3*sqrt(x)]-4=0

then replace x with u, and u equals sqrt(x)

therefore.....u^2-3u-4=0

then once factored you get u+1=0 with u=-1 and u-4=0 with u=4.

and since we substitued sqrt(x) with u we square both -1 and 4 which means x= 1 or 16

This I understand, but how do you do that method with a problem where the exponents are in fraction form? Like this one.....

x^(1/2)-4x^(1/4)+2=0

2. Originally Posted by some_nerdy_guy
Ok, so theoretically some equations can be treated as quadratic and we're supposed to solve by having u=b (the middle term) and multiply the middle term, and 'a,' by u.

For example......

x-[3*sqrt(x)]-4=0

then replace x with u, and u equals sqrt(x)

therefore.....u^2-3u-4=0

then once factored you get u+1=0 with u=-1 and u-4=0 with u=4.

and since we substitued sqrt(x) with u we square both -1 and 4 which means x= 1 or 16

This I understand, but how do you do that method with a problem where the exponents are in fraction form? Like this one.....

x^(1/2)-4x^(1/4)+2=0
$x^{\frac 12 } - 4 x^{ \frac 14} + 2 = \left( x^{ \frac 14 } \right)^2 - 4 \left( x^{ \frac 14} \right) + 2 = 0$

Let $u = x^{\frac 14}$

3. Ok, I see it now. Thank-you.