Question

2. On their last quiz, Seth and Maria were asked to solve the two radical equations below. Maria disagrees with Seth

solutions. Is Maria correct? Clearly justify your conclusions and correct any mistakes that possibly exist. (5pts)
Seth's solutions are given below:
a.
√3x - 2 = 9
3x - 2 = 3
3x = 5
X
४
||
513
b.
√√√x + 5 = -4
√√x = -9
x = -729

Answer 1

Maria is correct to disagree with Seth. The solution to the first equation is x = 27.67 and the second equation has no real solutions.

Step-by-step explanation:

The question asks us to evaluate Seth's solutions for two radical equations and determine if Maria's disagreement is correct. Let us check each of Seth's solutions.

Equation a:

1. Given equation: √(3x - 2) = 9
2. Squaring both sides: 3x - 2 = 81 (Seth's mistake: 9 squared is not 3.)
3. Adding 2 to both sides: 3x = 83
4. Dividing both sides by 3: x = 83/3 or x = 27.67 (rounded to two decimal places)

Equation b:

1. Given equation: √(√(√x + 5)) = -4
2. No real solutions exist because a square root cannot equal a negative number in the real number system (Seth's mistake: He assumed real solutions existed).

Maria is correct to disagree with Seth's solutions. For equation a, the correct step is to square 9 to get 81, not 3, and proceed accordingly. For equation b, there are no real solutions because a square root of a real number cannot be negative.