Răspuns:
S(4;16)
Explicație pas cu pas:
f(x) =y
in cazul de aici, x= 2+radical3; y=15 deci
a(2+rad3)/(2-rad3)+b/(2+rad3)=15
a(2+rad3)^2/(4-3)+b (2-rad3) /(4-3) =15
a(4+3+4rad3)+b(2-rad3) =15+
7a+2b+(4a-b)rad3=15+0*rad3
aici iar depaseste "putin " materia cele 2 nr sunt egale DACA si NUMAI daca partil lor rationale si, respectiv, irationale sunt egale
7a+2b=15 si
b=4a.........7a+8a=15......15a=15....a=1 apartine Z
b= 4*1=4 , apartine Z
deci f (x) =x/(2-rad3) +4/(2+rad3)
f(x) = x(2+rad3)+ 4(2-rad3)=
= 2x+8 + (x-4) rad3 apartine Q ;
pt orice x rational, 2x+8 va fi rational...ramane ca (x-4) *rad3=0 deci x-4=0...x=4
f(x) =2x+8= 2*4+8= 16
deci doar S(4;16)
