Question

DAU COROANA!!URGENT!!!!​

Answer 1

$a)~\Big(\sqrt{3} +1\Big)^2-\sqrt{3}\Big(4+3\sqrt{3} \Big) =\Big(\sqrt{3} \Big)^2 +2\cdot \sqrt{3} \cdot 1+1^2-4\sqrt{3} -3 \cdot 3=\\\\=3+2\sqrt{3} +1-4\sqrt{3} -9=-5-2\sqrt{3} \\\\ b)~\Big(\sqrt{5} -3\Big)^2+3\sqrt{5}\Big(2-\sqrt{5}\Big)=\Big(\sqrt{5} \Big)^2-2\cdot \sqrt{5} \cdot 3+3^2+6\sqrt{5} -3 \cdot 5=\\\\= 5-6\sqrt{5} +9+6\sqrt{5} -15=-1$

$c)~2\Big(\sqrt{2} +4\Big)^2-4\sqrt{2} \Big(3-\sqrt{2} \Big)=\\\\=2\Big(\Big(\sqrt{2}\Big)^2 +2 \cdot \sqrt{2} \cdot 4+4^2\Big)-12\sqrt{2} +4 \cdot 2=\\\\=2\Big(2+8\sqrt{2} +16\Big)-12\sqrt{2} +8=4+16\sqrt{2} +32-12\sqrt{2} +8=4\sqrt{2} +44$

$d)~3\Big(\sqrt{3} -1\Big)^2-\sqrt{3} \Big(\sqrt{3} -6\Big)-\Big(\sqrt{11}-\sqrt{2} \Big)\Big(\sqrt{11}+\sqrt{2} \Big) =\\\\=3\Big(\Big(\sqrt{3}\Big)^2-2 \cdot \sqrt{3} \cdot 1+1^2\Big)-3+6\sqrt{3} -\Big(\Big(\sqrt{11}\Big)^2-\Big(\sqrt{2} \Big)^2\Big)=\\\\=3\Big(3-2\sqrt{3} +1\Big)-3+6\sqrt{3} -(11-2)=9-6\sqrt{3} +3-3+6\sqrt{3} -9=0$

$e)~\Big(2\sqrt{5}+1\Big)^2+\Big(\sqrt{7} +\sqrt{2} \Big)\Big(\sqrt{7} -\sqrt{2} \Big)-\sqrt{80}=\\\\=\Big(2\sqrt{5}\Big)^2+2 \cdot 2\sqrt{5}\cdot 1+1^2+\Big(\sqrt{7}\Big)^2-\Big(\sqrt{2} \Big)^2-4\sqrt{5} =\\\\=20+4\sqrt{5} +1+7-2-4\sqrt{5} = 26$

$f)~\Big(5\sqrt{3} -7\Big)\Big(5\sqrt{3} +7\Big)-\Big(3\sqrt{3} -1\Big)^2-\sqrt{108} =\\\\=\Big(5\sqrt{3}\Big)^2-7^2-\Big(\Big(3\sqrt{3}\Big)^2-2 \cdot 3\sqrt{3} \cdot 1+1^2\Big)-6\sqrt{3} =\\\\= 75-49-\Big(27-6\sqrt{3} +1\Big)-6\sqrt{3} =75-49-27+6\sqrt{3} -1-6\sqrt{3} =-2$