SOLUTION: The sum of two number is 9. The sum of their squares is 101. Find the numbers

Question 451634: The sum of two number is 9. The sum of their squares is 101. Find the numbers
Answer by pedjajov(51) (Show Source): You can put this solution on YOUR website!
We have two numbers x and y.
Their sum is 9 ->
Sum of their squares is 101 ->

If we square first equation we get

Now we can replace with 101

From their sum we have that y=9-x, so

, multiply
, move everything on one side
, now we have quadratic equation and can find solutions for x

We get x = 10 or x = -1.
For x=10 we get y=9-x=9-10=-1.
For x=-1 we get y=9-(-1)=10

So two numbers are 10 and -1.

Check: , OK
, OK
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