The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers
The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
guys i figured it out after like 7 years
let x = bigger # and let y = smaller #
(1) x + y = 37 (2) x^2 + y^2 = 756.5
isolate 1.. y = -x +37.. and sub into 2
x^2 + (-x+37)^2 = 756.5
expand the bracket (it had a square so you write it twice) and FOIL
x^2 + x^2 -74x +1369 = 756.5
move the 756.5 onto other side of equation and change sign, then group like terms
2x^2 -74x +612.5
GCF
2(x^2 -37x+306.25)
factors that multiple to c and add to b
2(x^2 -12.5x -24.5x + 306.25)
2(x-12.5)(x-24.5)
out if bracket it is 12.5 and 24.5. if u wanna check plug these back into 1 and 2 equation stated above and thats it 😍
To solve this problem, we can set up a system of equations. Let's denote the two numbers as x and y.
From the given information, we have two equations:
Equation 1: x + y = 37
Equation 2: x^2 + y^2 = 756.5
To find the solution, we can use substitution or elimination methods. Let's go with substitution:
Solve Equation 1 for y:
y = 37 - x
Substitute the value of y in Equation 2:
x^2 + (37 - x)^2 = 756.5
x^2 + 1369 - 74x + x^2 = 756.5
2x^2 - 74x + 612.5 = 0
Now, we can solve this quadratic equation. Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case:
a = 2, b = -74, c = 612.5
Substituting the values:
x = (- (-74) ± √((-74)^2 - 4 * 2 * 612.5)) / (2 * 2)
x = (74 ± √(5476 - 4900)) / 4
x = (74 ± √576) / 4
Taking the square root:
x = (74 ± 24) / 4
Simplifying:
x1 = (74 + 24) / 4 = 98 / 4 = 24.5
x2 = (74 - 24) / 4 = 50 / 4 = 12.5
So, the two numbers are 12.5 and 24.5.
x+y = 37
x^2+y^2 = 765.5
x^2+(37-x)^2 = 765.5
2x^2 - 74x + 603.5
x^2 - 37x + 301.75 = 0
x = (37±9√2)/2
x = 12.1, 24.8
Hmmm. I don't get their answers either, but I'm a lot closer than you.
What did you do?