Question

Help..

Answer 1

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

Answer 2

@Nnesha @IrishBoy123

Answer 3

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...?

Answer 4

So I can do substitution? Okay

Answer 5

yes... that is the easiest method to solve this equation

when you get the solutions for u, then let the solutions equal \[x^{\frac{1}{3}}\]

Answer 6

then you can solve for x

Answer 7

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

Answer 8

u= -1/4 and u= 3

Answer 9

well it will give the real solutions...

I'd always treat questions of this type as quadratics....

so you need to solve

\[x^{\frac{1}{3}} = -\frac{1}{4},~~and~~~~, x^{\frac{1}{3}} = 1\]

Answer 10

So x= 32 and 27 correct?

Answer 11

Oops. -1/64, 27

Answer 12

yes that's a lot better

Answer 13

Thank you.