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

Question

jozelynw · Answer

@ganeshie8  can you help me pleaseeeee.

jozelynw · Answer

I know it has something to do with the negative index

anonymous · Answer

Is a negative index possible? Are you saying the problem is this?
$$\sqrt[-6]{x+3}+1=30$$

welshfella · Answer

its because of the negative  6 in the first equation
we get 
sqrt(x + 3) = 29/-6

squaring   gives x + 3 = (29/-6)^2

welshfella · Answer

in the second equation the right side is positive  ans a genuine solution is obtained

anonymous · Answer

@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

welshfella · Answer

the important thing to remember is that there are 2 square roots   a positive and a negative. So squaring both gives the same value.

jozelynw · Answer

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?

welshfella · Answer

you could call a coefficient

welshfella · Answer

like  8x:-   8 is the coefficient of x

jozelynw · Answer

ok

jozelynw · Answer

So, the negative number makes the equation extraneous . But y?

anonymous · Answer

$$-6\sqrt{x+3}+1=30$$
$$-6\sqrt{x+3}=29$$
$$\sqrt{x+3}=-\frac{ 29 }{ 6 }$$
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.