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Sub 505 Level|   Algebra|                  
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EducationAisle GMATinsight if for (2) we had \((x+1)^2 = x\) then would this statement be insufficient? Upon simplification we would get \( x^2 + x + 1 = 0\)
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Hoozan
EducationAisle GMATinsight if for (2) we had \((x+1)^2 = x\) then would this statement be insufficient? Upon simplification we would get \( x^2 + x + 1 = 0\)

Hoozan

For \( x^2 + x + 1 = 0\) compared with \( ax^2 + bx + c = 0\)

the Discriminant, \(b^2-4ac\) = \(1^2-4*1*1 = -3\)

Negative discriminant of a quadratic equation would mean that roots are NON-REAL i.e. NO SOLUTION
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x =?

Statement 1:
\(2x + 1 = 0\)
\(=> x = -1/2\)
Statement 1 is Sufficient.

Statement 2:
\((x + 1)^2 = x^2\)
\(x^2 + 2x + 1 = x^2\)
\(=> 2x + 1 = 0\) (cutting \(x^2\) on both sides)
\(=> x = -1/2\)
Statement 2 is also Sufficient.
So, Correct answer is option D.
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Hello from the GMAT Club BumpBot!

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