Question

Rationalize the denominator of:

The answer can be written as √5 - √2, where A, B, C, and D are integers, D is positive, and C is not divisible by the square of any prime. If the greatest common divisor of A, B, and D is 1, find A + B + D.
a) 8
b) 10
c) 12
d) 14

Answer 1

The student's question suggests calculating a quadratic formula or rationalizing a denominator. Without the full context, we provided the method for substituting values into the quadratic formula using the values a = 3, b = 13, c = -10, which involves calculating the discriminant and then applying the plus or minus operation before division by the denominator.

Step-by-step explanation:

The student appears to have provided information for rationalizing a denominator or solving a quadratic equation using values a = 3, b = 13, c = -10. However, the full context of the original problem is not present. A mentioned root expression is rationalized by multiplying by a conjugate, which alters the denominator but not the value. The correct method for the given information about a quadratic equation is to use the quadratic formula:

-b ± √(b² - 4ac)

When a = 3, b = 13, and c = -10, we substitute these into the formula resulting in:

-13 ± √(13² - 4 × 3 × (-10)) / (2 × 3)

This simplification can lead to the answer by first calculating the discriminant (the expression under the square root), then dividing by the denominator (2a) after applying the plus or minus operation