Question

Calculati utilizand formulele de calcul prescurtate
a) (5√3+√5)²-5√5·√12 =
b) (√6-√3)²+(2√2-3)(2√2+3)




Repede va rogggg.

Answer 1

           
$a) \\ (5\sqrt{3}+ \sqrt{5})^{2}-5\sqrt{5}* \sqrt{12} = \\ = [(5\sqrt{3})+ 2*5\sqrt{3}*\sqrt{5}+(\sqrt{5})^{2}]-5\sqrt{5}* \sqrt{4*3}= \\ =75 +10 \sqrt{3}\sqrt{5}+5 -5\sqrt{5}*2\sqrt{3}= \\ =75+5 +10 \sqrt{3}\sqrt{5}-10\sqrt{5}\sqrt{3} =\boxed{80}$



$b) \\ (\sqrt{6}- \sqrt{3})^{2}+(2\sqrt{2}-3)(2\sqrt{2}+3)= \\ =[(\sqrt{6})^{2}-2\sqrt{6}\sqrt{3}+(\sqrt{3})^{2}] +[(2\sqrt{2})^{2}- 3^{2}]= \\ =(6-2 \sqrt{6*3} +3)+(8 -9)= \\ =9-2 \sqrt{18}-1= \\ =8-2 \sqrt{9*2} =8-2*3 \sqrt{2} =\boxed{8-6\sqrt{2}}$