Question

10*x^(1/6)-3*x^(1/3)-3=0

Answer 1

Пусть $x^{\frac{1}{6}}=t$, тогда $x^{\frac{1}{3}}=(x^{\frac{1}{6}})^2=t^2$, при этом t ≥ 0.

$10t-3t^2-3=0\\3t^2-10t+3=0\\D_{/4}=25-3*3=16=4^2\\t_{1}=\frac{5-4}{3}=\frac{1}{3}; t_{2}=\frac{5+4}{3}=3\\x^{\frac{1}{6}}=\frac{1}{3}; x^{\frac{1}{6}}=3\\x=\frac{1}{729}; 729$

Ответ: $\frac{1}{729}; 729$

Answer 2

To solve the equation 10x^(1/6) - 3x^(1/3) - 3 = 0, we can use a substitution to simplify the equation. Let's substitute y = x^(1/6):

10y^2 - 3y^3 - 3 = 0

Now we have a cubic equation in terms of y. To solve this equation, we can use various methods, such as numerical methods or approximations. However, finding an exact solution for a cubic equation can be quite complex.

If you are looking for an approximate solution, you can use numerical methods or calculators that can solve equations numerically. Alternatively, you can use graphical methods to estimate the solutions.

If you provide a specific range or context for the variable x, I can assist you further in finding approximate solutions or applying specific methods.