Question

Fie numerele $\sqrt{2- \sqrt{2} }$ si $\sqrt{2+ \sqrt{2} }$
a) Calculati a*b 
b) Calculati (a+b)²
c) Aratati ca $\frac{b}{a} - \sqrt{2}$ ∈ Q
Multumesc

Answer 1

a=√(2-√2) 
b=√(2+√2)
axb=√(2-√2) x√(2+√2) =√(2-√2)(2+√2)=√(4-2)=√2
a²=2-√2
b²=2+√2
2ab=2√2
(a+b)²=a²+2ab+b²=2-√2+2+√2+2√2=4+2√2=2(2+√2)
b/a-√2=√(2+√2)/√(2-√2)-√2= [√(2+√2)]²/√(2-√2)√(2+√2)-√2 =(2+√2 )/√2 -√2 =
=(2+√2-2)/√2=1