Question

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

Answer 1

Hello!

Answer:

`\large \boxed{\sf x = (19 \pm √(365) )/(2)}`

Explanation:

We want to solve:

`\sf x^2=19x+1`

Set the equation to 0:

`\sf x^2-19x-1 =0`

It's a quadratic equation since it is in the form ax² + bx + c = 0.

To solve a quadratic equation, we have this formula:

`\sf x = (-b \pm √(b^2 - 4ac) )/(2a)`

In our equation, we have:

`\sf a = 1\\b =-19\\c=-1`

Let's solve our equation:

◼ Apply the quadratic formula:

`\sf x = (-(-19) \pm √((-19)^2 - 4(1)(-1)) )/(2(1))`

◼ Simplify the right side:

`\boxed{\sf x = (19 \pm √(365) )/(2)}`