Square root 3v1-x=-5

Question

Root squared to the 3rd over 1-x=-5

Answer 1

³√(1 - x) = -5

 

This is a cube-root equation.

 

Cube both sides of the equation to undo the radical sign.

 

1 - x = -125

 

   -x = -126

 

    x = 126

Answer 2

 

NOTE:  I interpreted this as 3 times the square root of (1 - x).

Arthur interpreted it as the cube root of (1-x).

So that is why our answers are different.

 

3√(1-X)=-5

  √(1-x) = -5/3

 

Squaring both sides,

 

   1 - x = (-5/3)²

   1 - x = 25/9

      - x = 25/9 - 1

      - x = 25/9 - 9/9

        x = 16/9

 

Check:

 

   3√(1 - 16/9) = -5

   3√(9/9 - 16/9) = -5

   3√(-7/9) = -5

   √(-7/9) = -5/3

   (√(-7/9))² = (-5/3)²

    -7/9 = 25/9

       FALSE

 

The equation has no real solution

 

Answer 3

(1-x)^(1/3)=-5

raise each side to the third power

1-x=-125

-x=-125-1

-x=-126

x=126