解：設x(x + y + z) = 30 – yz —— ➀
y(x + y + z) = 35 – zx —— ➁
z(x + y + z) = 42 – xy —— ➂
➀ – ➁ 得(x + y + z)(x – y)= -5 + z(x – y) => (x + y)(x – y) = -5 ——➃
由➀ x² + xy + yz + zx = 30 => x(x + y) + z(x + y) = 30 => (x + y)(x + z) = 30
同理由➁➂ (x + y)(y + z) = 35 ，(y + z)(x + z) = 42 ，可得 x + y = 5 或-5，y + z = 7 或 -7
<1> x + y = 5 由➃ 得 x – y = -1 => x = 2，y = 3 代入 y + z = 7，z = 4
<2> x + y = -5由➃ 得 x – y = 1 => x = -2， y = -3 代入 y + z = -7，z = -4
由<1><2> ( x , y , z ) = ( 2 , 3 , 4 ) 或 ( -2 , -3 , -4 )