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aratati ca x(x-2)²+2(3x²-1)-5x=(x-1)(x+1)(x+2),pentru orice x∈R

Răspuns :

⇒x(x²-4x+4)+6x²-2-5x=(x²-1)(x+2)
x³-4x²+4x+6x²-5x-x=x³+2x²-x-2
x³+2x²-x-2=x³+2x²-x-2
x³-x³+2x²-2x²-x+x=2-2
0=0   nu are solutii