Question

Aduceti la forma cea mai simpla expresia : (√ 3-1)²-2(√3+2,(5))+4|1-√ 3|

Answer 1

$\displaystyle ( \sqrt{3} -1)^2-2( \sqrt{3} +2,(5))+4|1- \sqrt{3} |= \\ = \sqrt{3} ^2-2 \cdot \sqrt{3} \cdot 1+1^2-2\left( \sqrt{3} + \frac{23}{9} \right)+4( \sqrt{3} -1)= \\ =3-2 \sqrt{3} +1-2 \sqrt{3} - \frac{46}{9} +4 \sqrt{3} -4=- \frac{46}{9}$