Question

4x^2/3 + 5x^1/3 - 6 = 0

What is the value of x?

Answer 1

please please help

Answer 2

Use the substitution \[ u=x^{1/3} \] Then you get a quadratic equation in u, which is easily solved.

Answer 3

i keep getting two answers but the answer sheet says only 1

Answer 4

one root at x = 27/64.

Answer 5

Why isn't there two roots to this though? How do you know?

Answer 6

You can show that this function is monotonically increasing (i.e. f'(x) > 0, for x > 0). Then using IVT, there can only be one root.