Răspuns:
1)
e) 3(5-2√6) ; 61-2√30 ; 13 - 4√3 ;
f) 3
g) 7
2)
e) 2
f) 1
g) -15
Explicație pas cu pas:
FORMULELE FOLOSITE:
1.a²- b² = (a+b)(a-b)
sau (a+b)(a-b) = a²- b²
2. (a-b)²= a²- 2·a·b + b²
e) (√6-3)² =(√6)² - 2·3·√6+3²=
=6 - 6√6 +9
= 15 - 6√6
=3(5-2√6)
(√5-√6)²=5²-2·√5·√6+6²
=25-2√30+36
=61-2√30
(2√3-1)²=(2√3)² - 2·2√3·1 + 1²=
=4·3 - 4√3 +1
=13 - 4√3
f) (√3-√2)(√3+√2) + (√5-3)(√5+3) =
(√3)²-(√2)² + (√5)²-(√3)² =
3-2 + 5-3= 1 + 2 = 3
g) (√6-√3)(√6+√3) - (√6-√10)(√6+√10)=
(√6)²-(√3)² - [ (√6)² - (√10)² ] =
6 - 3 - ( 6 - 10 ) =
3 - ( -4 ) = 3 + 4 = 7
2)
e) (2√3 + 3)(2√3 - 3) - (√2 - 1)(√2 + 1) =
(2√3)² - 3² - [ (√2)² - 1² ] =
4·3 - 9 - ( 2 - 1 ) =
12 - 9 - 1 = 3 - 1 = 2
f) (3 - √6)(3 + √6) + (√3 - 1)(√3 + 1) - ( 3 - √5)( 3 + √5) =
3²- (√6)² + (√3)² - 1² - [3² - (√5)² ] =
9 - 6 + 3 - 1 - ( 9 -5 ) =
3 + 2 - 4 = 5 - 4 = 1
g) (4 - 2√5)(4 + 2√5) + (3√2 - 5)( 3√2 + 5) - (√6 + √2)(√6 - √2) =
4² - (2√5)² + (3√2)² - 5² - [ (√6)² - (√2)² ] =
16 - 20 + 18 - 25 - ( 6 -2 ) =
-4 -7 - 4 = -15
