Find an approximate solution to the system of equations

x+y+z=2013

x y z = 2013

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We have

1) x + y + z = 2013

2) xyz = 2013

It is clear that one of the values, x for example, needs to be very close to 2013.

Using the golden ratio is a natural avenue to try here.

The golden ratio r is such that

1 + 1/r = r, (r + 1) = r^2 and

(r + 1) + 1/(r+1) = [(r+1)^2+1]/(r+1) = (r^2 + 2r + 2)/(r+1) = 3(r+1)/(r+1) = 3

Since (r + 1)[1/(r+1)] = 1 and 2013/2010 = 1.001493 (approx 1)

we can take

**x = 2010, y = (r + 1) = 2.6180 and z = 2013/[2010(r+1)] = 0.382****5**

**check: x + y + z = 2013.****0005**

### 1 Reply | Hide Replies ▲

I found the same results but the question for the fonction is numbers with no decimal like x= 1 , y =2 , z= 3 it couldnt be x=1,8 or like y=2,7 or z=3,4 for exemple, it has to be solid numbers

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