SOLUTION: 1. The sum of two numbers is seven. The sum of the squares of the two numbers is twenty nine. Find the two numbers. 2. The product of two consecutive even positive integers is

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Question 159560: 1. The sum of two numbers is seven. The sum of the squares of the two numbers is twenty nine. Find the two numbers.
2. The product of two consecutive even positive integers is one hundred twenty. Find the two integers.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

# 1

"The sum of two numbers is seven" translates to x%2By=7


"The sum of the squares of the two numbers is twenty nine" translates to x%5E2%2By%5E2=29


x%2By=7 Start with the first equation


y=7-x Subtract "x" from both sides


x%5E2%2By%5E2=29 Move onto the second equation


x%5E2%2B%287-x%29%5E2=29 Plug in y=7-x


x%5E2%2B49-14x%2Bx%5E2=29 FOIL


x%5E2%2B49-14x%2Bx%5E2-29=0 Subtract 29 from both sides


2x%5E2-14x%2B20=0 Combine like terms.


2%28x%5E2-7x%2B10%29=0 Factor out the GCF 2


2%28x-5%29%28x-2%29=0 Factor x%5E2-7x%2B10


x-5=0 or x-2=0 Set each value equal to zero


x=5 or x=2 Solve for "x" in each case.

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y=7-x Go back to the first equation


y=7-5 Plug in x=5


y=2 Subtract

So one pair of numbers is 5 and 2

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y=7-x Go back to the first equation


y=7-2 Plug in x=2


y=5 Subtract


So another pair of numbers is 2 and 5


So this means that the two numbers are 5 and 2 (or 2 and 5; the order does not matter)