Answer:
x = (7 ± √(41 + 4√13)) / 2
x = (7 ± √(41 - 4√13)) / 2
Explanation:
To find the value of x when Y is equal to 7 ± √13 in the equation Y = x² - 7x + 9, we can substitute the given values into the equation and solve for x.
Let's consider the two cases separately:
Case 1: Y = 7 + √13
Substituting this value into the equation:
7 + √13 = x² - 7x + 9
Rearranging the equation:
x² - 7x + 2 - √13 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 1, b = -7, and c = 2 - √13. Plugging these values into the quadratic formula, we get:
x = (7 ± √(49 - 4(1)(2 - √13))) / (2(1))
Simplifying further:
x = (7 ± √(49 - 8 + 4√13)) / 2
x = (7 ± √(41 + 4√13)) / 2
Case 2: Y = 7 - √13
Following the same steps as above, we get:
x = (7 ± √(41 - 4√13)) / 2