Question

8.4x^2/3 - 1.2x^1/3 = 24 i get x= 1.76 and x= -1.61 it is not right what am doing wrong? :(

Answer 1

`x=-4.25` and
`x=5.48`

Step by Step Explanation:

We have been given an equation
`8.4x^{(2)/(3)}-1.2x^{ (1)/(3)}=24`. We can convert this equation to a quadratic by making a substitution
`x^{(1)/(3)}=y`.

Therefore, our new equation becomes:

`8.4y^(2)-1.2y=24`

`8.4y^(2)-1.2y-24=0`

Upon using quadratic formula, we get:

`y=\frac{-b\pm\sqrt{b^(2)-4ac}} {2a}=\frac{1.2\pm\sqrt{(-1.2)^(2)-4(8.4)(-24)}} {2(8.4)}`

`y=\frac{1.2\pm√(1.44+806.4)} {16.8}=\frac{1.2\pm√(807.54)} {16.8}`

`y=-1.620,1.763`

These are the values of y, now we need to find the values of x, so we substitute these back into the equation
`x^{(1)/(3)}=y`.

`x^{(1)/(3)}=-1.620` gives us
`x=-4.25`

`x^{(1)/(3)}=1.763` gives us
`x=5.48`