a) \(\sqrt{11+4\sqrt{7}}-\sqrt{11-4\sqrt{7}}\)
\(=\sqrt{7+4\sqrt{7}+4}-\sqrt{7-4\sqrt{7}+4}\)
\(=\sqrt{\left(\sqrt{7}+2\right)^2}-\sqrt{\left(\sqrt{7}-2\right)^2}\)
\(=\left|\sqrt{7}+2\right|-\left|\sqrt{7}-2\right|\)
\(=\sqrt{7}+2-\sqrt{7}+2=4\)
a) \(\sqrt{11+4\sqrt{7}}-\sqrt{11-4\sqrt{7}}=\sqrt{\left(2+\sqrt{7}\right)^2}-\sqrt{\left(\sqrt{7}-2\right)^2}=2+\sqrt{7}-\sqrt{7}+2=4\)
b) \(A=\sqrt{11-4\sqrt{6}}-\sqrt{11+4\sqrt{6}}\)
\(\Rightarrow A^2=11-4\sqrt{6}-2\sqrt{\left(11-4\sqrt{6}\right)\left(11+4\sqrt{6}\right)}+11+4\sqrt{6}\)
\(A^2=22-2\sqrt{121-96}\)
\(A^2=22-2\sqrt{25}=22-2.5=12\)
\(\Rightarrow A=-\sqrt{12}\)(Chú ý \(A< 0\))
b) \(\sqrt{11-4\sqrt{6}}-\sqrt{11+4\sqrt{6}}\)
\(=\sqrt{11-2.2\sqrt{2}.\sqrt{3}}-\sqrt{11+2.2\sqrt{2}.\sqrt{3}}\)
= \(\sqrt{8-2.2\sqrt{2}.\sqrt{3}+3}-\sqrt{8+2.2\sqrt{2}.\sqrt{3}+3}\)
\(=\sqrt{\left(\sqrt{8}-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{8}+\sqrt{3}\right)^2}\)
\(=\sqrt{8}-\sqrt{3}-\sqrt{8}-\sqrt{3}=-2\sqrt{3}\)
\(\sqrt{x+y\sqrt{z}}\) hoặc \(\sqrt{x-y\sqrt{z}}\)
Dùng máy tính phương trình bậc 2
a = 1
\(b=-x\)
\(c=\frac{\left(y\sqrt{z}\right)^2}{4}\)
bấm máy tính có hai nghiệm X1 ; X2
\(=\sqrt{\left(\sqrt{X1}+\sqrt{X2}\right)^2}\) hoặc \(=\sqrt{\left(\sqrt{X1}-\sqrt{X2}\right)^2}\)
a)
\(=\sqrt{\left(\sqrt{7}+\sqrt{4}\right)^2}-\sqrt{\left(\sqrt{7}-\sqrt{4}\right)^2}\)
\(=|\sqrt{7}+2|-|\sqrt{7}-2|\)
\(=\sqrt{7}+2-\left(\sqrt{7}-2\right)\)
\(=4\)
b)
\(=\sqrt{\left(\sqrt{8}-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{8}+\sqrt{3}\right)^2}\)
\(=|\sqrt{8}-\sqrt{3}|-|\sqrt{8}+\sqrt{3}|\)
\(=\sqrt{8}-\sqrt{3}-\left(\sqrt{8}+\sqrt{3}\right)\)
\(=-2\sqrt{3}\)
