How many solutions are there to this equation? <mtable columnalign="right left right left right

crossoverman9b

crossoverman9b

Answered question

2022-06-22

How many solutions are there to this equation?
x 2 y 2 = z y 2 z 2 = x z 2 x 2 = y

Answer & Explanation

klemmepk

klemmepk

Beginner2022-06-23Added 16 answers

We have
x 2 y 2 = z y 2 z 2 = x z 2 x 2 = y
Adding the first two equations, we get that
x 2 z 2 = z + x z = x  or  x z = 1
Similarly, we get that
x = y  or  y x = 1
y = z  or  z y = 1
Hence, there are 8 possible choices of getting 3 equations. But the choice
x z = 1  and  y x = 1  and  z y = 1
gives no solution. The rest of the seen choices give the following solutions
( 0 , 0 , 0 ) ; ( 1 , 0 , 1 ) ; ( 0 , 1 , 1 ) ; ( 1 , 1 , 0 )
Roland Waters

Roland Waters

Beginner2022-06-24Added 6 answers

Sum both sides and get x + y + z = 0, so you're on a plane.
Further hint:
z = ( x 2 y 2 ) = ( x y ) ( x + y ) = z ( x y )

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