Răspuns
Explicație pas cu pas:
a=2/(√3 +1)+(√3 +1)²-√108-√(7-4√3)=
=2(√3 -1)/(√3 +1)(√3- 1)+3 +2√3+1-6√3-√(4-4√3+3)=
=2(√3 -1)/(3- 1)+3 +1-4√3-√(2-√3)²=
=2(√3 -1)/2+4-4√3-(2-√3)=
=√3 -1+4-4√3-2+√3=
=1-2√3 =-2,464 ⇒ a<1/2
[tex]\displaystyle\\a=\frac{2}{\sqrt{3}+1}+(\sqrt{3}+1)^2-\sqrt{108}-\sqrt{7-4\sqrt{3}}\\\\a=\frac{2(\sqrt{3}-1)}{3-1}+(3+2\sqrt{3}+1)-\sqrt{36\cdot3}-\sqrt{4+3-2\cdot2\cdot\sqrt{3}}\\\\a=\frac{2(\sqrt{3}-1)}{2}+(4+2\sqrt{3})-6\sqrt{3}-\sqrt{4-2\cdot2\cdot\sqrt{3}+3}\\\\a=(\sqrt{3}-1)+(4+2\sqrt{3})-6\sqrt{3}-\sqrt{2^2-2\cdot2\cdot\sqrt{3}+\Big(\sqrt{3}\Big)^2}\\\\a=\sqrt{3}-1+4+2\sqrt{3}-6\sqrt{3}-\sqrt{\Big(2-\sqrt{3}\Big)^2}[/tex]
[tex]\displaystyle\\a=\sqrt{3}-1+4+2\sqrt{3}-6\sqrt{3}-\Big(2-\sqrt{3}\Big)\\\\a=\sqrt{3}-1+4+2\sqrt{3}-6\sqrt{3}-2+\sqrt{3}\\\\a=-1+4-2+\sqrt{3}+2\sqrt{3}-6\sqrt{3}+\sqrt{3}\\\\a=1+4\sqrt{3}-6\sqrt{3}\\\\a=1-2\sqrt{3}~~~\text{a este numar negativ.}\\\\a<0<\frac{1}{2} \\\\\boxed{a<\frac{1}{2}}[/tex]
