Question

Se considera f:R -R ,f(x) =(1-√3)•x-√3
a)Rezolvati in multimea numerelor reale,inecuatia f(x)+1≥0
b)Determinati numerele rationale a si b pentru care punctul M(a+1;b√3)apartine graficului functiei f .

Answer 1

notatie >= , <= inseamna "mai mare sau egal" respectiv "mai mic sau egal"

f(x)+1 >=0
(1-radical(3))*x-radical(3)+1 >=0 , factor comun pe 1-radical(3);
(1-radical(3))*(x+1) >=0;

radica(3) este aproximativ 1.73 ,deci 1-radical(3) < 0
=> (x+1) <= 0 => x<=-1 => x apartine (-infinit,-1]

b) M apartine GF => f(a+1)=b*radical(3)
=> (1-radical(3))*(a+1)-radical(3)=b*radical(3)
=> a+1-a*radical(3)-radica(3)-radical(3)=b*radical(3)
=> b*radical(3)+a*radical(3)-a=1-2*radical(3)

radical(3)*(a+b)-a=-2*radical(3)+1

putem face sistem :

$\left \{ {{-a=1} \atop {(a+b)\sqrt{3} =-2 \sqrt{3} }} \right.$

=> a=-1  , inlocuind in a 2a ne da b=-1