Question

1.Cardinalul multimii A={x apartine N | 1001 ≤ x ≤ 2006 } este...
2.Daca a,b,c sunt cifre in baza zece si abc bara deasupra + bca bara deasupra + cab bara deasupra = 2664 ,atunci a+b+c=...
3.Daca 3x-12=x,atunci x³-x²=...
4.Daca impartind numarul natural x la numarul y obtinem catul 5 si restul 6,atunci la impartirea lui x+y la y+1 obtinem catul...si restul...
5.Propozitia: (3 +4)²=3²+4² are valoarea de adevar...

Answer 1

$1)~card~A=2006-1001+1=1006. \\ \\ 2) ~\overline{abc}+ \overline{bca} + \overline {cab}=2664 \Leftrightarrow \\ \Leftrightarrow 100a+10b+c+100b+10c+a+100c+10a+b=2664 \Leftrightarrow \\ \Leftrightarrow 111a+111b+111c=2664 \Leftrightarrow \\ 111(a+b+c)=111*24 \Rightarrow \boxed{a+b+c=24}. \\ \\ 3) ~3x-12=x \Rightarrow 3x-x=12 \Leftrightarrow 2x=12 \Rightarrow x=6. \\ x^{3}- x^{2} = x^{2} (x-1)=36*5=180.$

$4)~x=5y+6 \Rightarrow x+y=5y+6+y=6y+6=6(y+1) \Rightarrow catul=6;~ \\ restul=0.$

5) FALS!!!

(3+4)²=49 si 3²+4²=25.