Determine how many solutions has?

Question

Without solving the equations below, determine whether each equation has one positive solution, one negative solution, one solution at x=0  , two solutions, three solutions, or no solution.
 1. x^5 =3 
 2. x^−6 =−1/64  
 3. x^−1/3 =−2 
 4. x^−3 =9 
 5. x^2 =5 

Answer 1

1. To get a positive result, you would raise a positive number to the fifth power, so there is one positive solution.

 

2. Keep in mind that a negative exponent has nothing to do with negative numbers, so this is just  1/x⁶ = -1/64

    When you raise a real number to an even power, the result can't be negative, so this one has no solution.

 

3. This is 1 over the cube root of x. You can take the odd root of a negative number an get a negative result, so there is one negative solution.

 

4.  If you raise a positive number to an odd power, you get a positive result, so there is one positive solution.

 

5.  If you raise either a positive or a negative number to an even power, you get a positive result, so there are two solutions (one positive and one negative)