extraneous solutions

[silverdragon316]

I am having problems trying to figure out where to begin with this problem. The dirrections are: Use factoring to solve each equation for real values of the variable. the problem is: Z^3/2 -z^1/2=0. My book tells me the answer is 0,1. But I want to know how we get to the answer. Thank you. The book gives examples but adds adds another number. like
2m^2/3+3m^1/3-2=0

 

[Deleted member 4993]

I am having problems trying to figure out where to begin with this problem. The dirrections are: Use factoring to solve each equation for real values of the variable. the problem is: Z^3/2 -z^1/2=0. My book tells me the answer is 0,1. But I want to know how we get to the answer. Thank you. The book gives examples but adds adds another number. like
2m^2/3+3m^1/3-2=0

I assume your problem is

\(\displaystyle Z^{\frac{3}{2}} \, - \, Z^{\frac{1}{2}} \, = \, 0\)

substitute

\(\displaystyle U = Z^{\frac{1}{2}}\)

and use difference of cube formula

 

[Denis]

or factor: a^(1/2)(a - 1) = 0; so a^(1/2) = 0 OR a - 1 = 0 ; kapish?