Question

Utilizând formulele de calcul prescurtat efectuați :
a) (2+√5)²=
b) (√5+√6)²=
c) (√6-√2)²=
d) (5-√3)²=
e) (√5-√3)(√5+√3)=
f) (√6-2)(√6+2)

Answer 1

a)folosim formula (a+b)²=a²+2ab+b²
(2+√5)²=2²+2·2·√5+√5²=4+4√5+5=9+4√5

b)(√5+√6)²=√5²+2·√5·√6+√6²=5+2√30+6=12+2√30

(a-b)²=a²-2ab²+b²

c)(√6-√2)²=√6²-2·√6·√2+√2²=6-2√12+2=8-4√3

d)(5-√3)²=5²-2·5·√3+√3²=25-10√3+3=28-10√3

e)folosim formula (a+b)(a-b)=a²-b²
(√5-√3)(√5+√3)=√5²-√3²=5-3=2

f) (√6-2)(6+2)=√6²-2²=6-4=2