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Inverse deduction of mathematical theorem
Add 1 to the (1) equation to get: x? x? +x? +x? + 1= 12

Grouping common factor: x? (x? + 1)+(x? + 1)= 12; ∴(x? + 1)(x? + 1)= 12

(2). In Equation X? -( 12-m)x+m- 1=0, where a= 1, b=-( 12-m) and c=m- 1, the final product can be obtained by directly applying Vieta's theorem:

x? +x? =-b/a =-[-( 12-m)]/ 1 = 12-m; x? x? = c/a =(m- 1)/ 1 = m- 1。