Solve using qaudractic formula.Then use a calculator to aproximate to three decimal places,the solution as rational numbers x^2-4x+1=0
To solve the quadratic equation x^2 - 4x + 1 = 0 using the quadratic formula, we need to find the values of x that satisfy the equation. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In your case, a = 1, b = -4, and c = 1.
Now, let's substitute these values into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(1)(1))) / (2(1))
Simplifying further:
x = (4 ± √(16 - 4)) / 2
x = (4 ± √12) / 2
x = (4 ± 2√3) / 2
x = 2 ± √3
So, the solutions to the equation x^2 - 4x + 1 = 0 using the quadratic formula are x = 2 + √3 and x = 2 - √3.
To approximate these solutions as rational numbers to three decimal places, you can use a calculator. Just substitute the approximate value of √3, which is approximately 1.732, into the previous solutions:
x1 ≈ 2 + √3 ≈ 2 + 1.732 ≈ 3.732
x2 ≈ 2 - √3 ≈ 2 - 1.732 ≈ 0.268
Therefore, the approximate rational solutions to the equation x^2 - 4x + 1 = 0 to three decimal places are x ≈ 3.732 and x ≈ 0.268.