Question

(√2+√3)(2√2-√3)=?
2√5(√5-2√20)-√2(3√18-3)
Va rog!!..Multumesc!

Answer 1

$\displaystyle a) \left( \sqrt{2} + \sqrt{3} \right)\left(2 \sqrt{2} - \sqrt{3} \right)=2 \cdot 2 - \sqrt{6} +2 \sqrt{6} - 3 = \\ \\=4- \sqrt{6}+2 \sqrt{6} -3=1+ \sqrt{6}$
$\displaystyle b)2 \sqrt{5} \left( \sqrt{5} -2 \sqrt{20} \right)- \sqrt{2} \left(3 \sqrt{18} -3 \right)= \\ \\ =2 \sqrt{5} \left( \sqrt{5} -2 \cdot 2 \sqrt{5} \right)- \sqrt{2} \left(3 \cdot 3 \sqrt{2} -3\right)= \\ \\ =2 \sqrt{5} \left( \sqrt{5} -4 \sqrt{5} \right)- \sqrt{2} \left(9 \sqrt{2} -3\right)=2 \cdot 5-8 \cdot 5-9 \cdot 2+3 \sqrt{2} = \\ \\ =10-40-18+3 \sqrt{2} =3 \sqrt{2} -48$