SOLUTION: x+y=10,x*y=20 find the value of x,y

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Question 38365: x+y=10,x*y=20 find the value of x,y
Found 2 solutions by fractalier, venugopalramana:
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
From
x+y=10
x*y=20
let us solve for x in the first equation and substitute it into the second equation:
x = 10 - y
then
(10 - y)y = 20
10y - y^2 = 20
now solve
-y^2 + 10y - 20 = 0
y^2 - 10y + 20 = 0
Since this doesn't factor, we can use the quadratic formula:
y = (10 � sqrt(100 - 80)) / 2
y = (10 � 2sqrt(5)) / 2
y = 5 � sqrt(5)
These are your two numbers.

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
x+y=10...................................i
x*y=20 find the value of x,y
(x-y)^2=(x+y)^2-4y=10^2-4*20=100-80=20
x-y=sqrt(20)=2sqrt(5)....................................ii
i+ii
2x=10+2sqrt(5)
x=5+sqrt(5)
i-ii
2y=10-2sqrt(5)
y=5-sqrt(5)