Exercitiul 7si9. Va rog dau coroana

Răspuns:

n=100a+10a+a-100a+10b+b-3(b-a)

n=111a-100a-11b+3b-3a

n=8a-8b=>n=8(a-b)

n patrat perfect=>a-b=2 sau 8

a=b+2

b=1=>a=3

b=2=>a=4

b=3=>a=5

b=4=>a=6

b=5=>a=7

b=6=>a=8

b=7=>a=9

a=b+8

b=1=>a=9

_____________

3¹⁰¹:9⁵⁰=3¹⁰¹:(3²)⁵⁰=3¹⁰¹:3¹⁰⁰=3¹⁰¹⁻¹⁰⁰=3¹=3

[3⁵⁷:(3²)²⁵·3¹⁰]:3¹⁵=(3⁵⁷:3⁵⁰·3¹⁰):3¹⁵=(3⁵⁷⁻⁵⁰⁺¹⁰):3¹⁵=3¹⁷:3¹⁵=3¹⁷⁻¹⁵=3²=9

2·2²·2⁴³-2⁴⁶+[(3²)⁷⁴:3⁴³-3¹⁵ˣ⁶]⁰=2¹⁺²⁺⁴³-2⁴⁶=2⁴⁶-2⁴⁶+1=0+1=1

paranteza este la puterea 0 =>paranteza =1

9)

3¹⁰¹ : 9⁵⁰ = 3¹⁰¹ : 3²⁾⁵⁰ = 3¹⁰¹ : 3¹⁰⁰ = 3

[3⁵⁷ : (3²)²⁵ × 3¹⁰] : 3¹⁵ =

= (3⁵⁷ : 3⁵⁰ × 3¹⁰) : 3¹⁵

= (3⁵⁷⁻⁵⁰⁺¹⁰) : 3¹⁵

= 3¹⁷ : 3¹⁵

= 3¹⁷⁻¹⁵

= 3²

= 9

2×2²×2⁴³ - 2⁴⁶ + [(3²)⁷⁴ : 3⁴³ - 3¹⁵ˣ⁶]⁰ =

= 2¹⁺²⁺⁴³ - 2⁴⁶ + 1

= 2⁴⁶ - 2⁴⁶ + 1

= 0 + 1

= 1

7)

n = aaa - abb + 3(b - a)

= 100a + 10a + a - 100a - 10b - b + 3b - 3a

= 8a - 8b

= 8(a - b)

8x2 = 16 (patrat perfect) =>

a - b = 2

a = 2, b = 0

a = 3, b = 1

a = 4, b = 2

............................

a = 9, b = 7

8x8 = 64 (patrat perfect) =>

a - b = 8

a = 8, b = 0

a = 9, b = 1