The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
Sums of 5?
1 + 5
2 + 3
Which of those fit the other criterion?
the product of two numbers 24 and sum of their square is 52 find their sum
Well, this sounds like a math problem, but lucky for you, I'm a clown and I know how to solve it with a little twist of humor!
Let's call the first number "x" and the second number "y". According to the information given, we can set up two equations:
Equation 1: x + y = 5 <-- The sum of the two numbers is five.
Equation 2: x^2 + y^2 = 13 <-- The sum of the squares is thirteen.
Now, let the clown magic begin! 🎩
We can solve the first equation for x, which gives us x = 5 - y.
Substituting this value of x into the second equation, we get (5 - y)^2 + y^2 = 13.
Expanding and simplifying, we have 25 - 10y + y^2 + y^2 = 13.
Combining like terms, we get 2y^2 - 10y + 12 = 0.
Now, we can either attempt to factor or use the quadratic formula to solve for y. But remember, I'm a clown, so I'll use some magic to solve this equation! 🎩🤡
Presto! The value of y is 2.
Substituting y = 2 back into the first equation, we find x = 5 - 2, which gives x = 3.
So, the two numbers are 3 and 2. Ta-da! 🎉
And just in case you were looking for a comma-separated list, the answer is 3,2. Enjoy your math magic!
To find the two numbers, let's use algebra. Let's call the two numbers x and y.
We know that the sum of two numbers is five, so we can write the equation:
x + y = 5 -- (Equation 1)
We also know that the sum of the squares of the two numbers is thirteen, so we can write the equation:
x^2 + y^2 = 13 -- (Equation 2)
Now, we have a system of two equations with two unknowns. We can solve this system by substitution or elimination.
Let's solve it by substitution:
1. Rearrange Equation 1 to solve for x:
x = 5 - y
2. Substitute this value of x into Equation 2:
(5 - y)^2 + y^2 = 13
Expand the square:
25 - 10y + y^2 + y^2 = 13
Combine like terms:
2y^2 - 10y + 12 = 0
3. Divide the equation by 2 to simplify:
y^2 - 5y + 6 = 0
4. Factor the quadratic equation:
(y - 2)(y - 3) = 0
This gives us two possible values for y: y = 2 or y = 3.
5. Substitute these values back into Equation 1 to find the corresponding values of x:
For y = 2, x = 5 - 2 = 3.
For y = 3, x = 5 - 3 = 2.
So, the two numbers are 3 and 2.
Therefore, the answer is: 3, 2.
The numbers are 2 and 3
2+3=5
2^2=4
3^2=9
4+9=13