SOLUTION: The difference of two positive numbers is 5 and the sum of their squares is 157. Find the numbers. Please help me with this. I've tried writing an equation out to what it says

Question 221402: The difference of two positive numbers is 5 and the sum of their squares is 157. Find the numbers.
Please help me with this. I've tried writing an equation out to what it says but I'm completely lost.
Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"The difference of two positive numbers is 5" means that (note: this means that )

Also, because "the sum of their squares is 157" we know that

Start with the first equation.

Subtract x from both sides.

Multiply both sides by -1 and rearrange the terms.

Move onto the second equation.

Plug in

FOIL

Subtract 157 from both sides.

Combine like terms.

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

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

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to 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 possible solutions are or

However, it's stated that the numbers are positive. So the only answer is

Now just plug that value into and solve for 'y' to get --->

So the two numbers are and

Notice how 11-6=5. So their difference is 5

Also, take note how .

So this confirms our answer.
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