Question

tính x=\(\sqrt{97-56\sqrt{3}}+\sqrt{52+16\sqrt{3}}\)

       y=\(\sqrt{33+20\sqrt{2}}+\sqrt{24-16\sqrt{2}}\)

Answer 1

Ta có: \(x=\sqrt{97-56\sqrt{3}}+\sqrt{52+16\sqrt{3}}\)

\(=\sqrt{49-2\cdot7\cdot4\sqrt{3}+48}+\sqrt{48+2\cdot4\sqrt{3}\cdot2+4}\)

\(=\sqrt{\left(7-4\sqrt{3}\right)^2}+\sqrt{\left(4\sqrt{3}+2\right)^2}\)

\(=\left|7-4\sqrt{3}\right|+\left|4\sqrt{3}+2\right|\)

\(=7-4\sqrt{3}+4\sqrt{3}+2\)

\(=9\)

 

Answer 2

Làm luôn phần y :D

y = \(\sqrt{33+20\sqrt{2}}+\sqrt{24-16\sqrt{2}}\)

y = \(\sqrt{33+2.10\sqrt{2}}+\sqrt{24-2.8\sqrt{2}}\)

y = \(\sqrt{33+2.5.2\sqrt{2}}+\sqrt{24-2.4.2\sqrt{2}}\)

y = \(\sqrt{25+2.5.\sqrt{8}+8}+\sqrt{16-2.4.\sqrt{8}+8}\)

y = \(\sqrt{\left(5+\sqrt{8}\right)^2}+\sqrt{\left(4-\sqrt{8}\right)^2}\)

y = |5 + \(\sqrt{8}\)| + |4 - \(\sqrt{8}\)| 

y = 5 + \(\sqrt{8}\) + 4 - \(\sqrt{8}\)   (Vì 4 > \(\sqrt{8}\) nên 4 - \(\sqrt{8}\) > 0)

y = 9

Vậy y = 9

Chúc bn học tốt!