Х²-121х+5

To solve the equation \(x^2 - 121x + 5\) we can use the quadratic formula.

The quadratic formula states that for an equation in the form \(ax^2 + bx + c = 0\), the solutions for \(x\) can be found using the formula:

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

In this case, \(a = 1\), \(b = -121\), and \(c = 5\).

Plugging these values into the formula, we get:

\[x = \frac{-(-121) \pm \sqrt{(-121)^2 - 4(1)(5)}}{2(1)}\]

Simplifying:

\[x = \frac{121 \pm \sqrt{14641 - 20}}{2}\]

\[x = \frac{121 \pm \sqrt{14621}}{2}\]

Since the discriminant \(b^2 - 4ac = 14621\) is positive, we have two distinct real solutions. Therefore, we can write:

\[x_1 = \frac{121 + \sqrt{14621}}{2}\]

\[x_2 = \frac{121 - \sqrt{14621}}{2}\]

These are the solutions to the equation \(x^2 - 121x + 5\).