SOLUTION: The sum of two numbers is 25. The sum of their squares are 313. Find the numbers. My work: x+y=25 x^2+y^2=313 x=x y=25-x x^2+(25-x)^2=313 x^2+625+x^2-50x=313 2x^2-50

Algebra ->  Expressions-with-variables -> SOLUTION: The sum of two numbers is 25. The sum of their squares are 313. Find the numbers. My work: x+y=25 x^2+y^2=313 x=x y=25-x x^2+(25-x)^2=313 x^2+625+x^2-50x=313 2x^2-50      Log On


   

Question 158210: The sum of two numbers is 25. The sum of their squares are 313. Find the numbers.
My work:
x+y=25
x^2+y^2=313
x=x
y=25-x
x^2+(25-x)^2=313
x^2+625+x^2-50x=313
2x^2-50x+312=0
2(x^2-25x+156)=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll start where you left off


2x%5E2-50x%2B312=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-50, and c=312


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-50%29+%2B-+sqrt%28+%28-50%29%5E2-4%282%29%28312%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-50, and c=312


x+=+%2850+%2B-+sqrt%28+%28-50%29%5E2-4%282%29%28312%29+%29%29%2F%282%282%29%29 Negate -50 to get 50.


x+=+%2850+%2B-+sqrt%28+2500-4%282%29%28312%29+%29%29%2F%282%282%29%29 Square -50 to get 2500.


x+=+%2850+%2B-+sqrt%28+2500-2496+%29%29%2F%282%282%29%29 Multiply 4%282%29%28312%29 to get 2496


x+=+%2850+%2B-+sqrt%28+4+%29%29%2F%282%282%29%29 Subtract 2496 from 2500 to get 4


x+=+%2850+%2B-+sqrt%28+4+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%2850+%2B-+2%29%2F%284%29 Take the square root of 4 to get 2.


x+=+%2850+%2B+2%29%2F%284%29 or x+=+%2850+-+2%29%2F%284%29 Break up the expression.


x+=+%2852%29%2F%284%29 or x+=++%2848%29%2F%284%29 Combine like terms.


x+=+13 or x+=+12 Simplify.


So the answers are x+=+13 or x+=+12

Now use these values of x to find the values of y. Let me know if you have any questions.



Note: your answers should be (12,13) or (13,12) which means that the two numbers are 12 and 13