SOLUTION: The sum of two numbers is 11 The sum of the squares of the two numbers is 73, find the two numbers.

Question 200748: The sum of two numbers is 11
The sum of the squares of the two numbers is 73, find the two numbers.
Found 2 solutions by checkley77, RAY100:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
x+y=11 or x=11-y
x^2+y^2=73
(11-y)^2+y62=73
121-22y+y^2+y^2=73
2y^2-22y+121-73=0
2y^2-22y+48=0
2(y^2-11y+24)=0
2(y-8)(y-3)=0
y-8=0
y=8 ans. x=3 ans.
y-3=0
y=3 ans x=8 ans.
Proof:
3+8=11
3^2+8^2=73
9+64=73
73=73
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
(1) x +y =11
(2) x^2 + y^2 =73
.
from(1) y = (11-x)
.
subst into (2)
.
x^2 +(11-x)^2 =73
x^2 + (121 -22x +x^2 = 73
2x^2 -22x +48 =0
divide by 2
x^2 -11x +24 =0
factor
(x-8)(x-3) =0
x= 8 , 3
.
check
(1) 8+3=11,,,,ok
(2) 64 + 9 = 73 ,,,,,ok
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