We have the following equation:
x2 + 4x = - (y2 - 20)
Let's review step by step:
step 1:
x2 + 4x = -y2 + 20
Answer: OK
step 2:
x2 + 4x + 4 = -y2 + 20 - 4
Answer: Wrong
The correct step is:
x2 + 4x - 4 = -y2 + 20 - 4
Or equivalently:
x2 + 4x + 4 = -y2 + 20 + 4
Answer:
he did make an error in his work in step 2
A
rational number is any number that can be written as the
ratio between two other numbers i.e. in the form

Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are

,

,

and

so it makes sense to try and use those to build our number. In this case

works nicely.
Answer:The solution is in the attached file below
Step-by-step explanation:
Answer:

Step-by-step explanation:
Let

We factor 2 to obtain;

We factor the polynomial within the parenthesis by grouping.



We apply difference of two squares on the second factor: 

We now compare to;

It is now obvious that 