by: nora r.. problem suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y =...

By: Nora R POD Week #21 Problem #2

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By: Nora R.

POD Week #21

Problem #2

Problem

Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Problem:

First Step:

The first thing I did was try to figure out what I had to multiply x and y by to get 9.

I knew the product of x and y (xy) had to be 9 because it says in the problem that xy equals 9.

Page 4: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Second Step:

I know that since xy equals 9 I have to multiply two numbers to get 9.

So, I have two options, I can multiply 9×1 or 3×3. I guessed 9×1 first.

Page 5: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Third Step: So now what I did was solve the problem given (x²y + xy² + x + y) Since it doesn’t really matter what each variable is I just made

x=9 and y=1 So, now the new problem is - 9²(1) + 9(1)² + 9 + 1 - and I want to

see if this will equal 100.

Page 6: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Solving the Equation:

To solve this problem I just figured out what each section equals and then added them up to see if it equaled 100.

9²(1) + 9(1)² + 9 + 1 = ?9²= 8181 × 1 = 81

In the order of operations exponents come before multiplication so I have to do the exponent before multiplying anything, which pretty much means I have to do 1² first, then multiply that by 9. (PEMDAS)

1²= 11×9= 9

Page 7: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Fourth Step:

I added up all the numbers I got from the problem, to see if it equaled 100.

When I added them up, it did equal 100, so I knew I had the right numbers for x and y.

81 9 9 1 + 100

Page 8: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Final Step:

Now all I have to do to get my answer is solve the last problem giving with the variables I now have. (x=9, y=1)

The problem asked for me to solve the problem – x² + y² So I replace the variables with 9 and 1 to find the answer.

9² + 1²81 181 +1 = 82

Page 9: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Answer:

Once I solved that problem of 9² + 1² I got and answer of 82.

Page 10: By: Nora R.. Problem Suppose x and y are real numbers such that xy = 9 and x²y + xy² + x + y = 100. What is the integer value of x² + y²?

Any Questions?

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