Question

Решите уравнение (1-3x)^2+(3x-1)=0

Answer 1

Можно переписать как: (1-3х)²-(1-3х)=0, тогда (1-3х) можно вынести за скобки: (1-3х)(1-3х-1)=0; (1-3х)(-3х)=0; -3х=0; х=0; 1-3х=0; -3х=-1; х=1/3. Ответ: х=0; х=1/3.

Answer 2

I can help you solve equations and other math problems. To solve the equation $(1-3x)^2+(3x-1)=0$, we can use the following steps:

- Expand the squared term: $(1-3x)^2 = 1-6x+9x^2$ - Simplify the equation: $9x^2-12x+2=0$ - Use the quadratic formula to find the roots: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$, where $a=9, b=-12, c=2$ - Calculate the discriminant: $b^2-4ac = (-12)^2-4(9)(2) = 144-72 = 72$ - Find the roots: $x = \frac{12 \pm \sqrt{72}}{18} = \frac{2 \pm \sqrt{2}}{3}$ - Check the solutions by plugging them back into the original equation.

The solutions are $x = \frac{2 + \sqrt{2}}{3}$ and $x = \frac{2 - \sqrt{2}}{3}$. You can also use online calculators to solve equations, such as [Microsoft Math Solver](https://mathsolver.microsoft.com/ru/solver) or [Symbolab](https://ru.symbolab.com/solver/equation-calculator). These tools can show you the steps and the graph of the equation.