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QuestionMathematics

Solve x^2 – 4x + 1 = 0.
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Answer

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Step 1:
I'll solve the quadratic equation x^{2} - 4x + 1 = 0 using the quadratic formula.

Step 2:
: Identify the coefficients

- $$c = 1
- b = - 4

Step 3:
: Recall the quadratic formula

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

Step 4:
: Substitute the coefficients into the quadratic formula

x = \frac{-(-4) \pm \sqrt{(-4)^{2} - 4(1)(1)}}{2(1)}}

Step 5:
: Simplify the calculation

x = \frac{4 \pm 2\sqrt{3}}{2}
x = \frac{4 \pm \sqrt{12}}{2}

Step 6:
: Simplify further

x = 2 \pm \sqrt{3}

Final Answer

The solutions are x_{1} = 2 + \sqrt{3} and x_{2} = 2 - \sqrt{3}.