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Demonstrati ca:
(x² -x +1 )²=x la a 4 a -2x³ +3x ²-2x+1 oricare ar fi numarul real x


Răspuns :

(x²-x+1)² = x la a 4-a + x² + 1 -2x³ +2x² -2x = x la a 4a -2x³ +3x² -2x +1

folosesti formula (a+b+c)² = a²+b²+c²+2ab+2ac+2bc
(x²-x+1)² = x la a 4-a + x² + 1 -2x³ +2x² -2x = x la a 4a -2x³ +3x² -2x +1