Question

thực hiện phép tính :

a) A=\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)

b) B =\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)

c) C =\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)

giúp mjk bài này với :) mjk đang cần gấp lắm

Answer 1

a) \(A=\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\Rightarrow A^2=12-3\sqrt{7}+12+3\sqrt{7}-2\sqrt{\left(12-3\sqrt{7}\right)\left(12+3\sqrt{7}\right)}\Rightarrow A^2=24-2\sqrt{144-63}\Rightarrow A^2=24-18\Rightarrow A^2=6\Rightarrow A=\pm\sqrt{6}\)Ta có \(12-3\sqrt{7}< 12+3\sqrt{7}\Rightarrow\sqrt{12-3\sqrt{7}}< \sqrt{12+3\sqrt{7}}\Rightarrow\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}< 0\Rightarrow A< 0\)Vậy A=-6

b) \(B=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\Rightarrow B^2=4+\sqrt{10+2\sqrt{5}}+4-\sqrt{10+2\sqrt{5}}+2\sqrt{\left(4+\sqrt{10+2\sqrt{5}}\right)\left(4-\sqrt{10+2\sqrt{5}}\right)}\Rightarrow B^2=8+2\sqrt{16-10-2\sqrt{5}}\Rightarrow B^2=8+2\sqrt{5-2\sqrt{5}+1}\Rightarrow B^2=8+2\sqrt{\left(\sqrt{5}-1\right)^2}\Rightarrow B^2=8+2\sqrt{5}-2\Rightarrow B=\pm\sqrt{5+2\sqrt{5}+1}\Rightarrow B=\pm\left(\sqrt{5}+1\right)\)Ta có B>0⇒B=\(\sqrt{5}+1\)

c) \(C=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\Rightarrow C^2=3-\sqrt{5}+3+\sqrt{5}+2\sqrt{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}\Rightarrow C^2=6+2\sqrt{9-5}\Rightarrow C^2=6+4=10\Rightarrow C=\pm\sqrt{10}\)Ta có C>0⇒C=\(\sqrt{10}\)