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.Com
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) (Show Source): You can put this solution on YOUR website!
I'll start where you left off
Start with the given equation.
Notice we have a quadratic equation 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
Subtract from 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 answers are or
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
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