SOLUTION: If there is anyone that can help me solve this or I should say these problems it would be a huge help I have a exam that I'm studying for and cant spend any more time tring to get

Question 201016: If there is anyone that can help me solve this or I should say these problems it would be a huge help I have a exam that I'm studying for and cant spend any more time tring to get the solutions. Thank you to anyone nice enough to help me out!
#1a)The sum of the squares of two numbers is 128. The product of the numbers is 64. Find the numbers? (answer with a exact solution and in ordered pairs)
#1b) The difference between the squares of two numbers is 3. Twice the square of the first number increased by the square of the second number is 9. Find the numbers? (please put your solutions in the form of an ordered pair(s)
#1c) A 150 ffet of fence is available to enclose a 1125 square foot region in the shape of adjoining squares. With the sides of length X and Y. The big square has sides of length X and the small square has sides of length Y. Find X and Y?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction.

a)

"The sum of the squares of two numbers is 128" translates to

"The product of the numbers is 64" translates to

Start with the second equation.

Divide both sides by "x".

Move onto the first equation

Plug in

Square to get

Multiply EVERY term by the LCD to clear out the fractions.

Subtract from both sides.

Rearrange the terms.

Let . So

Replace with . Replace with

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "z":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the only solution (in terms of "z") is

Now recall that we let . So this means that and that or

--------------------------

Now let's find "y" when :

Go back to the first isolated equation.

Plug in

Reduce.

So when , giving the ordered pair (8,8)

--------------------------

Now let's find "y" when :

Go back to the first isolated equation.

Plug in

Reduce.

So when , giving the ordered pair (-8,-8)

===============================================================

Answer:

So the two ordered pair solutions are (8,8) and (-8,-8)

b)

"The difference between the squares of two numbers is 3" translates to

"Twice the square of the first number increased by the square of the second number is 9" translates to

Start with the first equation.

Add to both sides.

Move onto the second equation.

Plug in

Distribute

Subtract 6 from both sides.

Combine like terms.

Divide both sides by 3.

Reduce

or Take the square root of both sides (don't forget the "plus/minus")

or Take the square root of 1 to get 1

--------------------------

Now that we know "y", we can use these values to find "x".

Let's find "x" when :

Start with the given equation.

Plug in

Square 1 to get 1

Combine like terms.

or Take the square root of both sides

So the first two ordered pair solutions are (2,1) and (-2,1)

--------------------------

Start with the given equation.

Plug in

Square 1 to get 1

Combine like terms.

or Take the square root of both sides

So the next two ordered pair solutions are (2,-1) and (-2,-1)

========================================================

Answer:

So the four ordered pair solutions are:

(2,1), (-2,1), (2,-1) and (-2,-1)

c)

I'll let you do this one on your own. Let me know if you have questions.

If you have any questions, email me at jim_thompson5910@hotmail.com.
Check out my website if you are interested in tutoring.
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