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

1. JozelynW

@ganeshie8 can you help me pleaseeeee.

2. JozelynW

I know it has something to do with the negative index

3. anonymous

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

4. welshfella

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

5. welshfella

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

6. anonymous

@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

7. welshfella

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

8. JozelynW

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?

9. welshfella

you could call a coefficient

10. welshfella

like 8x:- 8 is the coefficient of x

11. JozelynW

ok

12. JozelynW

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

13. anonymous

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