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M03-18

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New post 09 Mar 2019, 05:21
Bunuel in this question, I took x = (x^2) and hence calculated the roots for (x^2)^2-2(x^2)+1 by the formula root(B^2-4ac) which turned out to be 0 and hence, I marked choice B. Am I missing something?
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New post 09 Mar 2019, 07:10
aalakshaya wrote:
Bunuel in this question, I took x = (x^2) and hence calculated the roots for (x^2)^2-2(x^2)+1 by the formula root(B^2-4ac) which turned out to be 0 and hence, I marked choice B. Am I missing something?



\((x^2)^2-2(x^2)+1 =0\)

\(x^2=\frac{2+\sqrt{4-4}}{2}\) --> \(x^2=1\) --> \(x=1\) or \(x = -1\);

\(x^2=\frac{2-\sqrt{4-4}}{2}\) --> \(x^2=1\) --> \(x=1\) or \(x = -1\).
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New post 01 May 2019, 04:36
Bunuel wrote:
aalakshaya wrote:
Bunuel in this question, I took x = (x^2) and hence calculated the roots for (x^2)^2-2(x^2)+1 by the formula root(B^2-4ac) which turned out to be 0 and hence, I marked choice B. Am I missing something?



\((x^2)^2-2(x^2)+1 =0\)

\(x^2=\frac{2+\sqrt{4-4}}{2}\) --> \(x^2=1\) --> \(x=1\) or \(x = -1\);

\(x^2=\frac{2-\sqrt{4-4}}{2}\) --> \(x^2=1\) --> \(x=1\) or \(x = -1\).



Hi Bunuel,

I was wondering how did you find the roots as illustrated above??
Is this some kind of formula??

Would appreciate your help!
THANKS
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New post 01 May 2019, 04:47
JIAA wrote:
Bunuel wrote:
aalakshaya wrote:
Bunuel in this question, I took x = (x^2) and hence calculated the roots for (x^2)^2-2(x^2)+1 by the formula root(B^2-4ac) which turned out to be 0 and hence, I marked choice B. Am I missing something?



\((x^2)^2-2(x^2)+1 =0\)

\(x^2=\frac{2+\sqrt{4-4}}{2}\) --> \(x^2=1\) --> \(x=1\) or \(x = -1\);

\(x^2=\frac{2-\sqrt{4-4}}{2}\) --> \(x^2=1\) --> \(x=1\) or \(x = -1\).



Hi Bunuel,

I was wondering how did you find the roots as illustrated above??
Is this some kind of formula??

Would appreciate your help!
THANKS


Solving and Factoring Quadratics:
http://www.purplemath.com/modules/solvquad.htm
http://www.purplemath.com/modules/factquad.htm

Hope it helps.
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M03-18  [#permalink]

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New post 01 Jul 2019, 22:46
Correct me if i'm wrong but this is simply the difference of squares?

X^4 -2x + 1 =0
(x^2-1)(x^2-1)=0
(x-1)(x+1)(x-1)(x+1) = 0
X= 1 or -1

Therefore there are 2 distinct roots.


I had dyslexia during the GMATClub test in which this question came up and I thought for some reason it was asking for that formula b^2-root 4ac... forget the name of it!
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New post 25 Jul 2019, 20:06
The statement becomes

(X^2 -1)^2=0

X=+-1

Thus, we have two values
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Re: M03-18   [#permalink] 25 Jul 2019, 20:06

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