Question

aratati ca urmatoarele propozitii sunt adevarate a) 1 supra √3-1= √ 3+1supra 2 b) 1supra √5-1=√5+1supra 4 c) 1supra √2+√3=√2-√3supra -1 d) 1 supra √7-2 =√7+2supra 3

Answer 1

a.1/√3-1=√3+1/2
1/√3+1=se amplifica cu √3-1;avem apoi:√3-1/(√3-1)(√3+1)=√3-1/3-√3+√3-1=√3-1/3-1=√3-1/2
b.1/√5-1=se amplifica cu √5-1;avem apoi:√5+1/(√5-1)(√5+1)=√5+1/5+√5-√5-1=√5+1/5-1=√5+1/4
c.1/√2+√3=se amplifica cu √2-√3;avem:√2-√3/(√2+√3)(√2-√3)=√2-√3/2-√6+√6-3=√2-√3/2-3=√2-√3/-1
d.1/√7-2=se amplifica cu √7+2 ;avem apoi √7+2/(√7+2)(√7-2)=√7+2/7-2√7+2√7-4=√7+2/7-4=√7+2/3