SOLUTION: Solve a) x^(1/2) - x ^(1/4) - 2 = 0 Can you please help me out? Thanks so much in advance:)

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Question 810579: Solve
a) x^(1/2) - x ^(1/4) - 2 = 0
Can you please help me out? Thanks so much in advance:)

Found 2 solutions by stanbon, Okeke_Christian:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
a) x^(1/2) - x ^(1/4) - 2 = 0
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This is a quadratic equation with variable x^(1/4)::
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Factor:
(x^(1/4)-2)(x^(1/4)+1) = 0
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x^(1/4) = 2 of x^(1/4) = -1
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x = 2^4 = 16
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Note:: x^(1/4) = -1 has an extraneous solution.
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Cheers,
Stan H.

Answer by Okeke_Christian(26) About Me  (Show Source):
You can put this solution on YOUR website!
x^(1/2) - x ^(1/4) - 2 = 0
x%5E%281%2F2%29+-x%5E%281%2F4%29+-+2+=+0
You raise each term by a power of four, like so:
%28x%5E%281%2F2%29%29%5E4+%28-x%5E%281%2F4%29%29%5E4+-2%5E4+=+0%5E4
The equation becomes:
x%5E2+%2B+x+%2B+16+=+0
...and just from me to you, I don't think that equation has any roots; SEE:
from x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a= 1; b= 1; c=16
Substitute
%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29+
%28-1+%2B-+sqrt%28+-63+%29%29%2F2+
...and personally, I don't think that
sqrt%28-63%29 will give anything besides a "MA ERROR".