What makes this equation -6√x+3 +1=30 extraneous apart from this one? (2√X+10 +3=23)

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What makes this equation -6√x+3 +1=30 extraneous apart from this one? (2√X+10 +3=23)

Mathematics
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@ganeshie8 can you help me pleaseeeee.
I know it has something to do with the negative index
Is a negative index possible? Are you saying the problem is this? \[\sqrt[-6]{x+3}+1=30\]

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Other answers:

its because of the negative 6 in the first equation we get sqrt(x + 3) = 29/-6 squaring gives x + 3 = (29/-6)^2
in the second equation the right side is positive ans a genuine solution is obtained
@welshfella That's how I read it at first, but then they mentioned a negative index and completely threw me. Your interpretation is the only one that makes sense
the important thing to remember is that there are 2 square roots a positive and a negative. So squaring both gives the same value.
I thought the the -6 was called the index that's why I said "I know it has something to do with the negative index". Sorry ,anyway what would the -6 be called then?
you could call a coefficient
like 8x:- 8 is the coefficient of x
ok
So, the negative number makes the equation extraneous . But y?
\[-6\sqrt{x+3}+1=30\] \[-6\sqrt{x+3}=29\] \[\sqrt{x+3}=-\frac{ 29 }{ 6 }\] The next step would be to square both sides, but the square root of a real number can't be negative. So whatever result you get by solving the equation won't be an actual solution.

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