The equation x² – 5x + 5 = 0 is a quadratic equation. To find its solution set, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In this case, the coefficients are as follows:
- a = 1
- b = -5
- c = 5
Next, we will calculate the discriminant, which is the part of the formula under the square root:
b² – 4ac = (-5)² – 4(1)(5)
Calculating this gives us:
- 25 – 20 = 5
Since the discriminant is positive (5), this indicates that there are two real and distinct solutions.
Now, substituting the values back into the quadratic formula:
x = (5 ± √5) / 2
This gives us two solutions:
- x₁ = (5 + √5) / 2
- x₂ = (5 – √5) / 2
Therefore, the solution set for the equation x² – 5x + 5 = 0 can be expressed as:
{(5 + √5) / 2, (5 – √5) / 2}
These solutions can be approximated as:
- x₁ ≈ 4.618
- x₂ ≈ 0.382
In conclusion, the solution set is:
{(5 + √5) / 2, (5 – √5) / 2} ≈ {4.618, 0.382}