Te rog mult .Ex 16.....

a)
(√3-2)^100.(√3+2)^100=
Se bazeaza pe formula (a+b) (a-b) =a²-b²
[(√3)²-2²] ^100=(3-4)^100=(-1)^100=1
^-puterea

a)
(a - b)²ⁿ = (b - a)²ⁿ

(√3 - 2)¹⁰⁰ = (2 - √3)¹⁰⁰

Expresia din enunț devine:


(2 - √3)¹⁰⁰(2 + √3)¹⁰⁰ = [(2 - √3)(2 + √3)]¹⁰⁰ = [2² - (√3)²]¹⁰⁰ =

= (4 - 3)¹⁰⁰ = 1¹⁰⁰ = 1

Am folosit formula (a - b)(a + b)  = a² - b²


c) (√8 - √2)²⁰ = (2√2 - √2)²⁰ = (√2)²⁰ = [(√2)²]¹⁰  = 2¹⁰  = 1024 .


d) (√3 - √12)¹⁶ = (√3 -2√3)¹⁶ = (-√3)¹⁶ = [(-√3)²]⁸ = 3⁸ = (3⁴)² =81² = 6561