Mathematics: Which are the solutions of x2 = 19x 1

Which are the solutions of x2 = 19x 1 - id21913829301, karatekats1

kevin2618

10.01.2022

For this case we have the following quadratic equation:

x ^ 2 = 19x + 1

Rewriting we have:

x ^ 2 - 19x - 1 = 0

Then, using the quadratic formula we have:

$x =\frac{-b+/-\sqrt{b^2-4ac}}{2a}$

Substituting values:

$x =\frac{-(-19)+/-\sqrt{(-19)^2-4(1)(-1)}}{2(1)}$

Rewriting:

$x =\frac{19+/-\sqrt{361+4}}{2}$

$x =\frac{19+/-\sqrt{365}}{2}$

Therefore, the solutions are given by:

$x =\frac{19+\sqrt{365}}{2}$

$x =\frac{19-\sqrt{365}}{2}$

The solutions of the equation are:

$x =\frac{19+\sqrt{365}}{2}$

$x =\frac{19-\sqrt{365}}{2}$

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