Question

Aratati ca numarul a=√3-1/√3+1 : 2-√3/2 apartine intervalului (√3 ; 2√3)

Answer 1

a=(√3-1/√3+1) : (2-√3/2) =
=(√3-1)(√3-1)/(√3+1)(√3-1) : (2-√3/2) =
=(3-2√3+1)/(3-1) × 2/( 2-√3) =
=(4-2√3)/2× 2/( 2-√3) =
=2(2-√3)/( 2-√3) =
=2

√3<2<2√3

Answer 2

a=(√3-1/√3+1) : (2-√3/2) = =(√3-1)(√3-1)/(√3+1)(√3-1) : (2-√3/2) = =(3-2√3+1)/(3-1) × 2/( 2-√3) = =(4-2√3)/2× 2/( 2-√3) = =2(2-√3)/( 2-√3) = =2 √3<2<2√3