Is 3,2 the correct answers to the bottom box, and how do you get the answer?

Question

1-1/x=6x^2

Answer 1

The rational equation 1 - (1/x) = 6x²

(x - 1)/x = 6x²

x - 1 = 6x³

6x³ - x + 1 = 0

Now solve the above cubic equation.

Now find zeros of polynomial f(x) = 6x³ - x + 1.

Graph

The points where it crosses the x axis  will give solutions to the polynomial function .

The graph crosses the x - axis at a point that would suggest a factor.

It crosses the x - axis at one point hence there are one real root.

x  = -0.65034

Use synthetic division to determine if the given value of x is a root of the polynomial.

Since f(-0.6503) = 0, x = -0.6503 is a zero.

The depressed polynomial is  6x² - 3.9018x + 1.5373

Since the depressed polynomial of this zero, 6x² - 3.9018x + 1.5373 = 0, is quadratic,

Use the Quadratic Formula to find the roots of the related quadratic equation ax² + bx + c = 0

a = 6, b = - 3.9018, c = 1.5373

Roots are

Solutions are x = - 0.6503 and x = 0.3251 ± 0.388i.