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x^2 = x , why x=1 AND x=0 ?

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x^2 = x , why x=1 AND x=0 ?

by tinglers » Sat Feb 21, 2009 8:18 am
GMAT OG DS #56

What is the value of XY?

(1) y= x+1

(2) y = x^2 +1

Answer is E since together x^2 = x can be 1 or 0

but why? My original impulsion is to divide both sides of x^2 = x by x to be simplified to x=1

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by ven4gmat » Sat Feb 21, 2009 8:33 am
x^2 = x...of course you can divided by x provided x is not equal to 0.

x^2 = x

x^2-x = 0

x(x-1) = 0

So x=0 or (x-1) = 0

Hence x could be 0 or 1
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by cramya » Sat Feb 21, 2009 9:38 am
but why? My original impulsion is to divide both sides of x^2 = x by x to be simplified to x=1
Perfectly natural impulsion. The reason why u cannot do this is because u may miss out on a solution of 0 as mentioned by Ven4gmat. Always try to get the varaibles on one side and take out the common term.

As u can see x can be 1 or 0 satisfying x^2 = x.

Regards,
CR
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