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

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Question 451634: The sum of two number is 9. The sum of their squares is 101. Find the numbers
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
We have two numbers x and y.
Their sum is 9 -> x%2By=9
Sum of their squares is 101 -> x%5E2%2By%5E2=101

If we square first equation we get

%28x%2By%29%5E2=9%5E2
x%5E2%2B2xy%2By%5E2=81

Now we can replace x%5E2%2By%5E2 with 101

2xy%2B101=81
2xy=-20
xy=-10

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

x%289-x%29=-10, multiply
9x-x%5E2=-10, move everything on one side
x%5E2-9x-10=0, now we have quadratic equation and can find solutions for x

x+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A%28-10%29+%29%29%2F%282%2A1%29+
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: 10%2B%28-1%29=9, OK
10%5E2%2B%28-1%29%5E2=100%2B1=101, OK