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Solving a System of Equations with Real Numbers (Posted on 2023-12-25)

Let x, y, z be real numbers that satisfy this system of equations:
• xy+4z=60
• yz+4x=60
• zx+4y=60
Let S be the set of possible values of x.
Determine the sum of the squares of the elements of S.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solve with Wolfram Alpha

| Comment 1 of 2

Wolfram Alpha lists these possibilities:

x = -10 and y = -10 and z = -10

x = 4 and y = 4 and z = 11

x = 4 and y = 11 and z = 4

x = 6 and y = 6 and z = 6

x = 11 and y = 4 and z = 4

The possible values of x are

(-10, 4, 6, 11)

The sum of their squares is 273.

Posted by Charlie on 2023-12-25 13:12:27

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