Question

so sánh -8 và -(√15 +√17)

Answer 1

\(8^2=64=32+32\\ \left(\sqrt{15}+\sqrt{17}\right)^2=32+2\sqrt{255}\)

\(32^2=1024>1020=\left(2\sqrt{255}\right)^2\\ \Rightarrow64>32+2\sqrt{255}\\ \Rightarrow8^2>\left(\sqrt{15}+\sqrt{17}\right)^2\\ \Leftrightarrow8>\sqrt{15}+\sqrt{17}\\ \Leftrightarrow-8< -\left(\sqrt{15}+\sqrt{17}\right)\)

Answer 2

Lời giải:

\((\sqrt{15}+\sqrt{17})^2=32+2\sqrt{15.17}=32+2\sqrt{(16-1)(16+1)}\)

\(=32+2\sqrt{16^2-1}< 32+2\sqrt{16^2}=64\)

\(\Rightarrow \sqrt{15}+\sqrt{17}< 8\)

\(\Rightarrow -(\sqrt{15}+\sqrt{17})> -8\)