Solve using qaudractic formula.Then use a calculator to approximate to three decimal places, the onlution as rational numbers. X^2-4x+1=0
To solve the quadratic equation x^2 - 4x + 1 = 0, we can use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -4, and c = 1. Let's substitute these values into the formula:
x = (-(-4) ± √((-4)^2 - 4*1*1)) / (2*1)
x = (4 ± √(16 - 4)) / 2
x = (4 ± √12) / 2
Now, simplify the expression inside the square root:
x = (4 ± √(4 * 3)) / 2
x = (4 ± 2√3) / 2
Next, we can simplify the expression further:
x = 2 ± √3
To approximate the solutions as rational numbers to three decimal places, we can use a calculator. Let's plug in the values:
x ≈ 2 + √3 ≈ 2 + 1.732 ≈ 3.732
x ≈ 2 - √3 ≈ 2 - 1.732 ≈ 0.268
Therefore, the solutions, approximated as rational numbers to three decimal places, are:
x ≈ 3.732
x ≈ 0.268.