Matematică
Leonetta
5

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

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(1) Răspunsuri
laru

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     

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