perplexus.info :: Just Math : Solving a System of Equations with Real Numbers

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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(x,y,z) = (-10,-10,-10), (6,6,6), (4,11,4), (11,4,4), or (4,4,11).
x takes on four possible values, so then set S is {-10,4,6,11} and the sum of the squares of it's elements is (-10)^2+4^2+6^2+11^2 = 273.
For an explanation,refer to the solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Brian Smith	2023-12-25 14:35:57
solve with Wolfram Alpha	Charlie	2023-12-25 13:12:27

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