Question

1. Aflati numerele naturale x si y stiind ca :
a) (2•x+3)•(2•x+4)= 56
b) (2•x+1)•(2•x+2)•(2•x+3)=720
c) (x-1)•(y+2)=13

2. Rezolvati ecuatiile
a) x+21•11=5⁴-19•3
b)x-(7²-11•4)=29•8-2la5
c)6•x:15+7²•5=15²+17•3-27
d) x-(29•5-12²)=25²-2•11•10
e)18:[(5²-5•x)•2-11]=2
f) 2014-{2015-[2014-(2013-x)]}=12
PS. Exercitiile caietul pentru vacanta clasa a V-a de marius perianu
Catalin miinescu si lucian petrescu

Answer 1

a) (2•x+3)•(2•x+4)= 56
4x²+6x+8x+12=56
4x²+14x-44=0
2x²+7x-22=0
Δ=7²+4*2*22=49+176=225
x₁=(-7+√225)/2*2=(-7+15)/4=2
x₂=(-7-√225)/2*2=(-7-15)/4=-22/4=-11/2=-5,5

b) (2•x+1)•(2•x+2)•(2•x+3)=720
720 =8*9*10
(2•x+1)=8   x=(8-1)/2=7/2
(2•x+2)=9   x=(9-2)/2=7/2
(2•x+3)=10   x=(10-3)/2=7/2


c) (x-1)•(y+2)=13
13=1*13
x-1=1     x=2
y+2=13  y=11

x-1=13     x=14    
y+2=1  y=-1

2. Rezolvati ecuatiile 
a) x+21•11=5⁴-19•3
x+231=625-57
x=337

b)x-(7²-11•4)=29•8-2⁵
x-(49-44)=232-32
x-5=200
x=205

c)6•x:15+7²•5=15²+17•3-27
2•x:5+49•5=225+51-27
2•x:5+245=249
2•x:5=4
2x=20
x=10

d) x-(29•5-12²)=25²-2•11•10
 x-(145-144)=625-220
 x-1=405
x=406
e)18:[(5²-5•x)•2-11]=2
18:[(25-5x)•2-11]=2
(25-5x)•2-11=9
50-10x=20
10x=30
x=3

f) 2014-{2015-[2014-(2013-x)]}=12
-{2015-[2014-(2013-x)]}=12-2014
2015-[2014-(2013-x)]=2002
-[2014-(2013-x)]=2002-2015
2014-(2013-x)=13
-(2013-x)=13-2014
2013-x=2001
x=12