Question

Macar 2 ex sa ma ajutati dau coronita.

Answer 1

6) a) x + 2√6 =8√6
x=8√6-2√6
x=6√6

b) 3√2-x=8√2
-x=8√2-3√2
-x=5√2 = ) x = -5√2

c) 2(x+√3)=4√3+x
2x+2√3=4√3+x
2x-x=4√3-2√3
x=2√3

d) 2(x+1)-2√7=3(x+√7)
2x+x-2√7=3x+3√7
2x-3x=3√7-2+3√7
-x=5√7-2
x=5√7-2

_______________________________________

9) a) 3√5 - /√5-√6/-(-3√6) =
= 3√5-(√6-√5)+3√6 =
= 3√5-√6+√5+3√6  = 4√5 +2√6

b) 4√6-(2√7-√6+/√6-√7/) =
= 4√6 -(2√7-√6+√7-√6)=
4√6 -(3√7 -2√6) = 6√6-3√7


c) 4-√2-(/2-√2/+3√2) =
= 4-√2-(2-√2+3√2) =
= 4-√2-(2+2√2)=
= 4-√2-2-2-2√2 = 2-3√2


d) 8√10 - (/√10-3/ + /4-√10/) =
= 8√10 - (√10 -3+4-√10) =8√10 -1 

e) /√3+√2/-/√3-√2/+/√2-√3/ =
= √3+√2-(√3-√2)+√3-√2 =
= √3-√3+√2-√3 = √2+√3
________________________________________

8) a) √a² < 5 = ) a ∈ (-5,5)

b) √a < a < √25 = ) a ∈ (2,5)

c) -√16 ≤ a < -√3 =) a ∈ (-4 , √3 )

d) -3 ≤ a ≤ √9 = ) a ∈ (-3,3) 

e) a² ≤ 9 = ) a ∈ (-3,3)

f) 3 ≤ a² < 17 = ) a ∈ ( -√17,√3 ) ∪ ( √3 , √17 ) 

Answer 2

5) Notez Ma= media aritmetica

a) Ma= ( 2√3 +5√2 + √2 - 2√3) : 2 = 6√2 / 2 = 3√2

b) Ma = ( 3√5+ √6 +5√6-√5) : 2 = (2√5 + 6√6) /2 = 2 (√5 + 3√6) /2 = √5 + 3√6

c) Ma = (3√2 + √3 + 1+ √2 + 5√3 - 1) / 2 = ( 4√2 +6√3)/2 = 2(2√2 + 3√3)/2 =
= 2√2 + 3√3

d) Ma = ( √7 + 2√3 + 4√3 - √7) : 2 =  6√3 : 2 = 3√3

e) Ma = ( 2 - 3√3 + 4 + 5√2) : 2 = ( 6 + 2√3) : 2 = 2 ( 3 + √3) /2 = 3+√3

f) Ma = ( √2 + 3√3 + √3 - √2 + √3) : 2 = 5√3 /2 = 2,5√3

g) Ma= ( √2 - √3 - 3√2 + √2) / 2 = (- √2 - √3) /2 = - ( √2 + √3)/2

h) Ma = (  √11 - √13 + 4√13 + √11) / 2 = (2√11 - 3√13) /2


6) a)
x + 2√6 =8√6
x=8√6-2√6
x=6√6

b)
3√2-x=8√2
x = 3√2 - 8√2
x = - 5√2

c)
2(x+√3)=4√3+x
2x+2√3=4√3+x
2x-x=4√3-2√3
x=2√3

d)
2(x+1)-2√7=3(x+√7)
2x+2-2√7=3x+3√7
2x-3x=3√7+2√7-2
-x=5√7-2
x=2 - 5√7

7)
A= {1, 2, 3, 4}, deoarece x∈N, x < √17
B= { 4, 5}, deoarece y ∈N, √10 < y < √25
C = { √9 = 3}, deoarece z ∈N;  √8 < z < √15

8)
a) √a² < 5 ⇒ a = ( - 2, -1, .....+2)
b)  √4 < a < √25  ⇒ a = (3, 4)
c)  a² ≤ 9  ⇒ a = [ - 3, -2, -1, 0, 1, 2, 3]
d)  - 3 ≤ l a l ≤ 9  ⇒ a = [ - 3, -2, -1, 0, 1, 2, 3,......9]



9)
a) 3√5 - l√5-√6l-(-3√6) =
= 3√5-(√6-√5)+3√6 =
= 3√5-√6+√5+3√6  =
= 4√5 +2√6

b)
4√6-(2√7-√6+l √6-√7 l) =
= 4√6 -(2√7-√6+√6 -√7)=
=4√6 -√7  =


c)
4-√2-(l 2-√2 l+3√2) =
= 4-√2-(2-√2+3√2) =
= 4-√2-(2+2√2)=
= 4-√2-2-2√2 =
= 2-3√2


d)
8√10 - (l √10-3 l + l 4-√10 l) =
= 8√10 - (√10 -3+4-√10) =
= 8√10 -1 

e)
l √3+√2 l - l √3-√2 l +l √2-√3 l =
= √3+√2-√3-√2 +√2-√3 =
 = √2-√3