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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!
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.
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 ! )
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,
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