Question

1.Demonstrati ca numarul n=2007+2x(1+2+3+......+2006) este patrat perfect
2.Fie multimea B={21;1,04;2,(6);3/8}.Multimea elementelor A={x | radical din x apartine lui B}
3.Precizati radacina patrata a numarului n cu aproximatie de o unitate (prin lipsa si prin adaos_ daca:n=27
4.Fie Sa suma elementelor multimii: A={n |n=3k,k apartine M},unde M={-1,-2,-3,....,-100},si Sb suma elementelor multimii B={n | n=4k,k apartine M}.Calculati Sa/Sb
5.Comparat numerele reale,introduncand factorii sub radicali: 3 radical 29 si 7 radical 24

Answer 1

1) n=2007+ 2* (1+2006)/2=

n=2007+(1+2006)

n=2007+2007

n=2007²-este pp

2)√21=4,58
√1,04= √1 intreg 4/100= √ 114/100= 10,67/10= 1,067
√2,(6)= √2 intregi 6/9= √2 intregi 2/3=  √8/3= 2,82/1,73= 1,63
√3/8= 1,73/2,82=  0,61

A={0,61 ; 1,067; 1,63; 4,58}

3)√27= 5,196

aproximare prin lipsa de o unitate 5,196 =4,196  ≈4 ≈1

aproximare prin adaos de o unitate 5,196 =6,196 ≈6 ≈10

4)M= (-1-100)*100/2= -101 *50= -5050

Sa= 3* (-5050)= -15150

Sb= 4* (-5050)= -20200

Sa/Sb= -15150/-20200= 1515/2020= 303/404=  0,75

5) 3√29  casuta de comparat 7√24
     √261    < √1176

     3√29 < 7√24