Question

Which are the solutions of x^2 = 19x + 1?

A. 19 ± √19
B. 19 - √365, 19 + √365
C. 0 - √19, √19
D. -19 = √1365 - 19 + √1365"

Answer 1

The solutions of the equation x² = 19x + 1 are (19 + √357)/2 and (19 - √357)/2.

Step-by-step explanation:

To find the solutions of the equation x² = 19x + 1, we can use the quadratic formula. The quadratic formula is given by:

x = (-b ± √(b² - 4ac))/(2a)

For this equation, a = 1, b = -19, and c = -1. Substituting these values into the quadratic formula, we get:

x = (-(-19) ± √((-19)² - 4(1)(1)))/(2(1))

Simplifying further, we have:

x = (19 ± √(361 - 4))/2

x = (19 ± √357)/2

So the solutions of the equation are:

x = (19 + √357)/2

x = (19 - √357)/2