Question

Urgent !!!!! 35 puncte !!

Answer 1

1)
a = 9×8+8×1 - 25(25×4-9×11)^2000
a = 72+8 - 25×(100-99)^2000
a = 80 - 25 ×1
a = 80-25
a = 55

b =30^n+1 - 30^n - 29×5^n×6^n
b =30^n × 30 - 30^n - 29×30^n
b = 30^n(30 - 1 - 29)
b = 30^n × 0
b = 0

c = (1+2^1002 -2^0) : (2^91)^11
c = (1+2^1002-1) : 2^1001
c = 2^1002 : 2^1001
c = 2^1
c = 2

in ordine crescatoare:
b ; c ; a .


2)
2^(x+1) = 2^17
x+1 = 17
x = 16

35^(x+4) : 7^(x+4) = 5^6
7^(x+4) × 5^(x+4) : 7^(x+4) = 5^6
5^(x+4) = 5^6
x+4 = 6
x = 2

3^3x : 27 = 3^99
3^3x : 3^3 = 3^99
3^(3x-3) = 3^99
3x-3 = 99 |:3
x - 1 = 33
x = 34

7 × 7^3 × 7^5 ×...× 7^33 = 7^(x^2)
7^(1+3+5+...+33) = 7^(x^2)
7^(17×34:2) = 7^(x^2)
7^(17 ×17) = 7^(x^2)
17^2 = x^2
x = 17

5^(2x+1) × 5^(x+3) = 25^5
5^(2x+1+x+3) = (5^2)^5
5^(3x+4) = 5^10
3x+4 = 10
3x = 6
x = 2



3)
35^7 = 35^6 × 35 = 35^6(3^3+2^3) =

= (35^2)^3 × (3^3+2^3) =
= (35^2 ×3)^3 + (35^2 × 2)^3

65^22 = 65^21 × 65 =
= (65^7)^3 × (1^3 + 4^3) =
= (65^7 × 1)^3 + (65^7 × 4)^3 =
= (65^7)^3 + (65^7 × 4)^3

45^45 = 45^44 × 45 =
= (45^22)^2 × (6^2 + 3^2) =
= (45^22 × 6)^2 + (45^22 × 3)^2


29^11 = 29^10 × 29 =
= (29^5)^2 × (2^2 + 5^2) =
= (29^5 × 2)^2 + (29^5 × 5)^2