1. a/b=5/7
a= 5b/7
(7a+2b)/(17a-3b)= (7 × 5b/7 +2b)/17×5b/7 -3b =
=(5b+2b) / [(85b-21b)/7]= 7b/(64b/7) =49b/64b=49/64
49/64 = (7/8)²
2
271 unde 27=3³ si 1 e patrat perfect si
641 unde 64=4³ si 1 e patrat perfect
4 2x5y
45x
45=
2025
46x
45=
2070
47x
45=
2115
48x
45=
2160
49x
45=
2205
singurul nr este 50x
45=
2250
51x
45=
2295
52x
45=
2340
58 x45=
2610
62x
45=
2790
63x
45=
2835
5. 2^n×3^n×5^n +2^n×15^n×14 +3^n×10^n×2+170 =
=2^n×3^n×5^n (2⁰×3⁰x5⁰+ 14 +2+170)=
=2^n×3^n×5^n (1+ 14 +2+170)=
=2^n×3^n×5^n ×187=
=2^n×3^n×5^n ×11× 17 ⇒ deci divizibil cu 17
6. (a+b)/2=5 a+b=10
(c+d+e)/3=25 c+d+e =75
(f+g+h+i+j)/5 =200 f+g+h+i+j =1000
(a+b+c+d+e+f+g+h+i+j)/10 = (1000+75+10)/10=1085/10 =108,5
11 E=490·(-1)^n+2 + 9·(-1)^n+4+ 8·(-1)^n+3+ 7·(-1)^n+2+6·(-1)^n+1+5·(-1)^n =
=1^n( 490·(-1)² + 9·(-1)⁴+ 8·(-1)³+ 7·(-1)²+6·(-1)¹+5·(-1)⁰ =
=1^n( 490 + 9- 8+ 7-6+5) = 1^n × 497 = 1^n × 71× 7 = deci divizibil cu 7
10. d=distanta
de la 11:59 la 25:02 sunt 3 h si 3 min
deci drumul dus intors a durat 3 ore = 3x60x60=10800 secunde
d/2+d/6=10800
4d=64800
d=16200 m = 16,2 km
dus a facut 16200 m: 2m/s= 8100 sec = 135 min = 2 ore si 15 min.
intaors a facut 16200 m: 6m/s= 2700 sec =45 min
7 in jurul unui punct masori de 7 ori 103 grade
7x103=721 grade
360x2=720
721-720=1 grad
12. 10x-3=25y+2
x=(25y+5)/10=(5y+1)/2
10x-3+25y+2+20x+20x=360
50x+25y=361
50× (5y+1)/2+25y=361
125y+25+25y=361
150y=361-25=336
y=2,24
x= (5×2,24+1)/2= 6,1
x+y= 6,1+2,24=8,34
m(<AOB)= 10×6,1-3=58
m(<COD)= 25×2,24+2=58
m(<AOC)=m(<BOD)=20× 6,1=122
9 x/2015
1/59
1/17
se aduc la acelasi numitor
17x2015/59x17x2015 = 34255/2021045
59x2015/17x59x2015=118885/2021045
118885-34255=84630 de fractii
