Răspunsuri

2014-01-16T17:23:01+02:00
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2014-01-16T17:26:18+02:00
 Notatie: a^2= a ridicat la patrat

|(12+13i) / (6+ai)|=2 <=>
|(12+13i)(6-ai) / (36+a^2)|=2 <=>
|(72-12ai+78i+13a) / (36+a^2|=2 <=>
[(72+13a)^2]/[(36+a^2)^2] + [(78-12a)^2]/[(36+ a^2)^2] = 4 <=>
(72+13a)^2 + (78-12a)^2 = 4(36+a^2)^2 <=>
Dupa calcule ( sunt prea mari ca sa le scriu aici :D ), rezulta :
4a^4 - 25a^2 - 6084 = 0
 Notam: a^2=t , t>=0
4t^2- 25t - 6084=0
Calculam delta =97969= 313^2
t1=(25+313)/8= 42.25
t2=(25-313)/8 < 0 ( nu indeplineste conditia pusa initial de noi)

t=42.25 => a^2=42.25 => a=6.5 
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