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Priyanka2011
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Exponents .. logic.. please explain ! 25 Jul 2012, 08:24
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Hai all

I am just not getting this logic.. just help me with this


(x+4)^1/2^2 = 3

Now if we simplify this is : x+4 = 3 so I get x=-1

However I can see in the solution that [ x+4 ]= 3 (i.e modulus)

so x=-1 or -7

Please explain !



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mikemcgarry
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Exponents .. logic.. please explain ! 25 Jul 2012, 08:36
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Priyanka2011
Hai all

I am just not getting this logic.. just help me with this

(x+4)^1/2^2 = 3

Now if we simplify this is : x+4 = 3 so I get x=-1. However I can see in the solution that [ x+4 ]= 3 (i.e modulus) so x=-1 or -7

Please explain!
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I would love to help you with this, but first of all, I need to know what is the source of this question? And more importantly, I need it to be written in proper mathematical syntax. What you have is sloppy and unclear. What you have written I interpret as . . .

[(x+4)^1/2]^2 = 3

but that has a solution of only x = -1. The problem

[(x+4)^2]^(1/2) = 3

would have a solution of both x = -1 and x = -7, but that doesn't appear consistent with what you have written.

If you clarify the problem, with proper mathematical syntax, I will be better able to help you. Here are a couple blog articles that might help you.
https://magoosh.com/gmat/2012/exponent-p ... -the-gmat/
https://magoosh.com/gmat/2012/exponent-p ... -the-gmat/

Mike :-)
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Priyanka2011
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Exponents .. logic.. please explain ! 25 Jul 2012, 08:46
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Hai.. sorry for the bad usage of syntax.. yeah what you have inferred is absolutely right !

[(x+4)^2]^(1/2) = 3

If the problem is as above, how is x=-7 ( i get the other part being simple ! )
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Exponents .. logic.. please explain ! 25 Jul 2012, 09:29
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Priyanka2011
Hai.. sorry for the bad usage of syntax.. yeah what you have inferred is absolutely right !

[(x+4)^2]^(1/2) = 3

If the problem is as above, how is x=-7 ( i get the other part being simple ! )
Show more

Well, there are a few ways to approach this ---- the straightforward algebraic way would be to solve for x -----

[(x+4)^2]^(1/2) = 3
undo the power of 1/2 by squaring both sides
(x+4)^2 = 9
take a square root of both sides, remembering the +/- sign
x+4 = +/-3, which means x = -1 and x = -7

The equation u^2 = 9 must have two solutions, u = +3 and U = -3, because (3)^9 and also (-3)^2 = 9

Another way to go about it is to plug in the solution x = -7 to verify that it satisfies the equation.
[(x+4)^2]^(1/2) = [(-7+4)^2]^(1/2) = [(-3)^2]^(1/2) = 9^(1/2) = 3
so, x = -7 checks out --- it is a valid solution for this equation.

Notice, even though u^2 = 9 has two solutions, the positive root and the negative root, the expression 9^(1/2) has only one output, just the positive root.

Does all this make sense? Please let me know if you have any further question.

Mike :-)



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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