Answer:
[tex]x=-4.25[/tex] and [tex]x=5.48[/tex]
Step by Step Explanation:
We have been given an equation [tex]8.4x^{\frac{2}{3}}-1.2x^{ \frac{1}{3}}=24[/tex]. We can convert this equation to a quadratic by making a substitution [tex]x^{\frac{1}{3}}=y[/tex].
Therefore, our new equation becomes:
[tex]8.4y^{2}-1.2y=24[/tex]
[tex]8.4y^{2}-1.2y-24=0[/tex]
Upon using quadratic formula, we get:
[tex]y=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}=\frac{1.2\pm\sqrt{(-1.2)^{2}-4(8.4)(-24)}} {2(8.4)}[/tex]
[tex]y=\frac{1.2\pm\sqrt{1.44+806.4}} {16.8}=\frac{1.2\pm\sqrt{807.54}} {16.8}[/tex]
[tex]y=-1.620,1.763[/tex]
These are the values of y, now we need to find the values of x, so we substitute these back into the equation [tex]x^{\frac{1}{3}}=y[/tex].
[tex]x^{\frac{1}{3}}=-1.620[/tex] gives us [tex]x=-4.25[/tex]
[tex]x^{\frac{1}{3}}=1.763[/tex] gives us [tex]x=5.48[/tex]
