Destinyyyy one year ago Help..

1. Destinyyyy

Find the real solutions of the equation. 4x^2/3 -11x^1/3 -3=0

2. Destinyyyy

@Nnesha @IrishBoy123

3. campbell_st

ok.. so this is an equation that can be written as a quadratic use a substitution $u = x^{\frac{1}{3}}$ so the equation is $4u^2 - 11u - 3 = 0$ this can be factored to (4u + 1)(u - 3) = 0 so then solve for u... does that make sense so far...?

4. Destinyyyy

So I can do substitution? Okay

5. campbell_st

yes... that is the easiest method to solve this equation when you get the solutions for u, then let the solutions equal $x^{\frac{1}{3}}$

6. campbell_st

then you can solve for x

7. Destinyyyy

Yes I know that.. I assumed I couldn't solve that way since it didnt say I could

8. Destinyyyy

u= -1/4 and u= 3

9. campbell_st

well it will give the real solutions... I'd always treat questions of this type as quadratics.... so you need to solve $x^{\frac{1}{3}} = -\frac{1}{4},~~and~~~~, x^{\frac{1}{3}} = 1$

10. Destinyyyy

So x= 32 and 27 correct?

11. Destinyyyy

Oops. -1/64, 27

12. campbell_st

yes that's a lot better

13. Destinyyyy

Thank you.