Question

3x(36x^2+12x+1)=10(6x+1)

Answer 1

3*(6x+1)^2 = 10(6x+1) сокращаем 6х+1
3*(6x+1)=10
6х+1 = 10/3
6х=10/3-1 = 3 1/3 - 1 = 2 1/3
х = 7/(3*6)=7/18

Answer 2

To solve the equation, let's first expand and simplify both sides:

3x(36x^2 + 12x + 1) = 10(6x + 1)

Expanding the left side:

3x * 36x^2 + 3x * 12x + 3x * 1 = 10(6x + 1)

Simplifying:

108x^3 + 36x^2 + 3x = 60x + 10

Now, let's move all the terms to one side of the equation to set it equal to zero:

108x^3 + 36x^2 + 3x - 60x - 10 = 0

Now, combine like terms:

108x^3 + 36x^2 - 57x - 10 = 0

At this point, the equation is in the form of a cubic equation: ax^3 + bx^2 + cx + d = 0.

Unfortunately, cubic equations are generally more challenging to solve analytically than quadratic equations. In this case, we can use numerical methods or calculators to find approximate solutions.

One approach is to use numerical methods like the Newton-Raphson method, but it requires an initial guess for the solution. Another approach is to use a graphing calculator or an online graphing tool to find the approximate solutions visually.

Without an initial guess for the solutions, I'm unable to provide exact numerical answers. However, using a graphing calculator, you can plot the function y = 108x^3 + 36x^2 - 57x - 10 and look for its x-intercepts (where y = 0) to get approximate solutions.

Please note that the solutions might be irrational or complex numbers, depending on the coefficients in the cubic equation.