Question

AM NEVOIE VA ROG PANA MAINE, DAU 100 DE PUNCTE, MACAR UN EXERCITIU VA ROG

Answer 1

Răspuns:

Explicație pas cu pas:

4. Formula: (a+b)²=a²+2ab+b²

a) (2+√3)²=2²+2·2·√3+(√3)²=4+4√3+3=7+4√3

b) (√5+2)²=(√5)²+4√5+4=5+4√5+4=9+4√5

c) (√7+3)²=(√7)²+6√7+9=16+6√7

d) (3+√6)²=9+6√6+(√6)²=9+6√6+6=15+6√6

e) (√5+5)²=(√5)²+10√5+25=35+10√5

f) (√3+√2)²=(√3)²+2·√3·√2+(√2)²=3+2√6+2=5+2√6

g) (√6+√5)²=(√6)²+2·√6·√5+(√5)²=6+2√30+5=11+2√30

h) (√15+√3)²=(√15)²+2√15·√3+(√3)²=15+2√45+3=18+2√45

i) (√10+√6)²=(√10)²+2·√10·√6+(√6)²=10+2√60+6=16+2√60=16+2√(4·15)= 16+2·2√15

j) (√12+1)²=(√12)²+2√12+1=12+2√12+1=13+2√12

k) (2a+a√3)²=(2a)²+2·2a·a√3+(a√3)²=4a²+4a²√3+3a²=7a²+4a²√3

l)(√12+√18)²=(√12)²+2·√12·√18+(√18)²=12+2√216+18=30+2·6√6=30+12√6

5. Formula: (a-b)²=a²-2ab+b²

a) (4-√5)²=4²-2·4·√5+(√5)²=16-8√5+5=21-8√5

Pe celelalte le faci aplicand formula data la inceputul exercitiului.

6. Formula: (a+b)(a-b)=a²-b²

a) (√2+1)(√2-1)=(√2)²-1²=2-1=1

Pe celelalte le faci aplicand formula data la inceputul exercitiului.

7.

a) (x+1)²=x²+2x+1

Pe celelalte le faci aplicand formulele date la inceputul exercitiilor 4 si 5.

8.

a) [(1/2)·x+1]²=[(1/2)·x]²+2·(1/2)·x·1+1²=x²/4+2·x/2+1=x²+x+1

Pe celelalte le faci aplicand formulele date la inceputul exercitiilor 4 si 5.