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Y = x² - 7x+9
7 ± √13
[?]
X =

User Ktiu
by
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1 Answer

2 votes

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

User Darren Reid
by
7.7k points