Determine the sum of the positive valued solution to the simultaneous equations:

Question

xy = 15, yz = 35,zx = 21

Answer 1

We can solve this system of equations by multiplying all three equations together:

(xy)(yz)(zx) = 15 * 35 * 21
xyz * xyz * xyz = 15 * 35 * 21
(xyz)^2 = 15 * 35 * 21
xyz = √(15 * 35 * 21)

We know that xyz is positive because all three variables (x, y, and z) are positive.

Now, if we divide each equation by the corresponding variable, we get:

xy / x = y
yz / y = z
zx / z = x

Substituting the given values, we have:

y = 15 / x
z = 35 / y
x = 21 / z

Substituting these values into the equation xyz = √(15 * 35 * 21), we get:

(21 / z) * (15 / (15 / x)) * (35 / (35 / y)) = √(15 * 35 * 21)
21 * x * 35 * y * 15 * z = √(15 * 35 * 21)^2
(21 * 35 * 15) * xyz = 15 * 35 * 21
xyz = 1

Therefore, the positive valued solution to this system of equations is xyz = 1.

The sum of the positive valued solution is 1 + 1 + 1 = 3.