Question

Select the two values of x that are roots of this equation.
x2+1=5x
02=52
2
5+V21
X=
2
02=ニ1-/19
• x==1+v19

Answer 1

To solve the equation \( x^2 + 1 = 5x \), we first rearrange it into standard quadratic form:

\[
x^2 - 5x + 1 = 0
\]

Next, we can apply the quadratic formula:

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

Here, \( a = 1 \), \( b = -5 \), and \( c = 1 \). Plugging in these values:

1. Calculate \( b^2 - 4ac \):

\[
(-5)^2 - 4(1)(1) = 25 - 4 = 21
\]

2. Now apply the quadratic formula:

\[
x = \frac{-(-5) \pm \sqrt{21}}{2(1)} = \frac{5 \pm \sqrt{21}}{2}
\]

Thus, the two roots are:

\[
x = \frac{5 + \sqrt{21}}{2} \quad \text{and} \quad x = \frac{5 - \sqrt{21}}{2}
\]

These are the two values of \( x \) that are roots of the equation \( x^2 + 1 = 5x \).