Question

Se consideră E(x)=x³+(x+2)²+2(x-4)(x+4)-2x+28,x Apartine R ,Aratati ca E(n) este multiplu de 6,pentru oricare n apartine N​

Answer 1

E(x)=x³+(x+2)²+2(x-4)(x+4)-2x+28

E(x)=x³+x²+4x+4+2x²+8x-8x-32-2x+28

E(x)=x³+3x²+2x=x(x+1)(x+2) => produs de 3 termineni consec.=>E(x)=M6

=>E(n)=M6, oricare ar fi n ap N