Question

4) Calculați: a) – 4 – (– 5) – 2∙(– 3) =
b) 2∙{– 8 – 3∙[– 7 – 2∙(18 – 12 – 9)]} =
c) (– 3)2 – (– 1)6 – (– 80) =
d) (– 32)5 ∙ (+ 3)5 : (– 92)3 + (– 33) =
e) (– 1)2 ∙ (– 1)4 ∙ (– 1)6 ∙ ... ∙ (– 1)60 =
f) – 2 ∙ (– 1)n – 3 ∙ (– 1)2n+1 – 4 ∙ (– 1)n+1




Va rog repede

Answer 1

Răspuns:

Explicație pas cu pas:

4) Calculați: a) – 4 – (– 5) – 2∙(– 3) =-4+5+6=1+6=7

b) 2∙{– 8 – 3∙[– 7 – 2∙(18 – 12 – 9)]} =2·{-8-3·[-7-2·(6-9)]}= 2·{-8-3·[-7-2·(-3)]}=

2·[-8-3·(-7+6)]= 2·[-8-3·(-1)]= 2·(-8+3)=2·(-5}=-10

c) (– 3)2 – (– 1)6 – (– 80) =(-3)²-(-1)⁶-(-80)=9-1+80=8+80=88

d) (– 32)5 ∙ (+ 3)5 : (– 92)3 + (– 33) =(-3²)⁵∙(+3)⁵:(-9²)³+(-3³)= 3¹⁰∙3⁵:(3⁴)³+(-3³) = 3¹⁵:3¹²+(-3³)=3³-3³=0

e) (– 1)2 ∙ (– 1)4 ∙ (– 1)6 ∙ ... ∙ (– 1)60 =(-1)²∙(-1)⁴∙(-1)⁶∙.....∙(-1)⁶⁰=1∙1∙1∙ ... ∙1=1

f) – 2 ∙ (– 1)n – 3 ∙ (– 1)2n+1 – 4 ∙ (– 1)n+1= -2∙(-1)ⁿ-3∙(-1)²ⁿ⁺¹-4∙(-1)ⁿ⁺¹

Aici sunt 2 cazuri, n= numar par si n = numar impar.

I. Daca n= numar par, atunci 2n+1=impar si n+1=impar  

-2∙(-1)ⁿ-3∙(-1)²ⁿ⁺¹-4∙(-1)ⁿ⁺¹=-2∙1-3∙(-1)-4∙(-1)= -2+3+4=1+4=5

II. Daca n= numar impar, atunci 2n+1=impar si n+1=par  

-2∙(-1)ⁿ-3∙(-1)²ⁿ⁺¹-4∙(-1)ⁿ⁺¹=-2∙(-1)-3∙(-1)-4∙1=2+3-4=5-4=1