Question

Решите уравнение: 4x^3-x^2=0

Answer 1

4x³-x²=0

x²(4x-1)=0

x²=0 => x=0

4x-1=0 => x=1/4

Ответ: 0; 1/4

Answer 2

I can help you solve this cubic equation. Here are the steps:

- First, we need to factor out the common term x^2 from the equation. This gives us x^2(4x-1)=0. - Next, we can use the zero product property to find the values of x that make the equation true. This means that either x^2=0 or 4x-1=0. - Solving for x, we get x=0 or x=1/4 as the possible solutions. - To check our answers, we can plug them back into the original equation and see if they satisfy it. For x=0, we get 4(0)^3-(0)^2=0, which is true. For x=1/4, we get 4(1/4)^3-(1/4)^2=0, which is also true. - Therefore, the equation has two real solutions: x=0 and x=1/4.

You can learn more about how to solve cubic equations from these sources: [4 Ways to Solve a Cubic Equation - wikiHow](https://www.wikihow.com/Solve-a-Cubic-Equation), [Solving Cubic Equations – Methods & Examples - The Story of Mathematics](https://www.storyofmathematics.com/solving-cubic-equations/), [Cubic Polynomial - Formula | Solve Cubic Equation - Cuemath](https://www.cuemath.com/algebra/cubic-polynomials/), [Cubic equations - mathcentre.ac.uk](https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-cubicequations-2009-1.pdf).