Respuesta :
Answer:
Step 2: (z+3)=20/2
Step-by-step explanation:
Given Eliza's Work:
[tex](z + 3)^2$ - 2 = 18\\Step 1:(z + 3)^2= 20\\$Step 2:\\Step 3: z + 3 = 10\\Step 4: z = -13 or z = 7[/tex]
For Eliza to have obtained z+3 = 10 in step 3, she erroneously divided the right hand side of step 1 by 2. Therefore, what she wrote in her step 2
Step 2: (z+3)=20/2
However, the correct solution is:
[tex](z + 3)^2$ - 2 = 18\\Step 1:(z + 3)^2= 20\\$Step 2:\sqrt{(z + 3)^2} =\pm \sqrt{20} \\$Step 3: z + 3 = \pm 2\sqrt{5} \\$Step 4: z = -3+ 2\sqrt{5}$ or z = -3 - 2\sqrt{5}[/tex]
Answer:
Eliza could have written √(z + 3)² = √20 in Step 2
Step-by-step explanation:
For step 2, we have
Step 2: (z + 3) = 20/2
However, Eliza could have written from (z + 3)² - 2 = 18,
Step 1 (z + 3)² = 18 + 2 = 20
Adding 2 to both sides
Step 2: √(z + 3)² = √20
Finding the square root of both sides
Step 3: z + 3 = √20
Rationalizing the left hand side of the equation
Step 4: √20 - 3
Subtracting 3 from both sides
Therefore, the step missing in step 2 was the finding of the square root of both sides of the equation
Which was taken as the division of both sides by 2.
