Answer:

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Explanation:

To solve the quadratic equation x² + (a + b)/(a + a/b)x + 1 = 0, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = (a + b)/(a + a/b), and c = 1.

First, simplify the value of b:

b = (a + b)/(a + a/b)

To remove the fraction in the denominator, multiply both the numerator and denominator by b:

b = (b(a + b))/(ab + a)

Now, plug these values into the quadratic formula:

x = (-(a + b)/(ab + a) ± √(((a + b)/(ab + a))² - 4(1)(1))) / (2(1))

Now, you can simplify and solve for x:

x = (-(a + b) ± √((a + b)² - 4(ab + a))) / 2

x = (-(a + b) ± √(a² + 2ab + b² - 4ab - 4a)) / 2

x = (-(a + b) ± √(a² - 2ab + b² - 4a)) / 2

x = (-(a + b) ± √((a - b)² - 4a)) / 2

So, the solutions for x are:

x₁ = (-(a + b) + √((a - b)² - 4a)) / 2

x₂ = (-(a + b) - √((a - b)² - 4a)) / 2