The given equation can be solved by first isolating x on one side of the equation. After simplifying, we can substitute values of x into the equation to see if they satisfy it.The equation
has no real solution.
The provided mathematical equation (shown below) features the variable x and a constant chi (χ)
![[x(\frac{1}{\sqrt[x]{\chi^(3)}})-(x^(x-2))/(x)=0]](https://img.qammunity.org/2023/formulas/mathematics/college/9rax4fuky84to2s1zynh2idc1lzmtde1rr.png)
To solve for the solution, we can isolate x on one side of the equation:
![[x(\sqrt[x]{\chi^(3)})=(x^(x-2))/(x)]](https://img.qammunity.org/2023/formulas/mathematics/college/cr37lfgg0gymcu6lia4pwssgpax5n3776x.png)
Simplifying the equation, we get:
![[\sqrt[x]{\chi^(3)}=x^(-1)]](https://img.qammunity.org/2023/formulas/mathematics/college/mgv9lhuo8ptsh0w8yoxsnfg47kl4jnkydk.png)
Since we have to find the value of x that satisfies the equation, we can now substitute x by a value and check whether the equation holds true.
Let's assume x = 2. Substituting this value in the above equation, we get:
![[\sqrt[2]{\chi^(3)}=2^(-1)]\\[\sqrt[2]{\chi^(3)}=(1)/(2)]](https://img.qammunity.org/2023/formulas/mathematics/college/1750kgcelfs7vka6c8svuke3z5uj8jkaza.png)
Since
does not equal 1/2, we can conclude that x = 2 is not a solution to the given equation. We can continue this process by substituting different values of x until we find a value that satisfies the equation.