Trục căn thức ở mẫu:
a) \({1 \over {\sqrt 3 + \sqrt 2 + 1}}\)
b)\({1 \over {\sqrt 5 - \sqrt 3 + 2}}\)
Gợi ý làm bài
a) \(\eqalign{
& {1 \over {\sqrt 3 + \sqrt 2 + 1}} = {1 \over {\sqrt 3 + (\sqrt 2 + 1)}} \cr
& = {{\sqrt 3 - (\sqrt 2 + 1)} \over {\left[ {\sqrt 3 + (\sqrt 2 + 1)} \right]\left[ {\sqrt 3 - (\sqrt 2 + 1)} \right]}} \cr} \)
\( = {{\sqrt 3 - \sqrt 2 - 1} \over {3 - {{(\sqrt 2 + 1)}^2}}} = {{\sqrt 3 - \sqrt 2 - 1} \over {3 - (2 + 2\sqrt 2 + 1)}} = {{\sqrt 3 - \sqrt 2 - 1} \over { - 2\sqrt 2 }}\)
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\( = {{ - \sqrt 2 (\sqrt 3 - \sqrt 2 - 1)} \over {2{{(\sqrt 2 )}^2}}} = {{ - \sqrt 6 + 2 + \sqrt 2 } \over 4}\)
b) \({1 \over {\sqrt 5 - \sqrt 3 + 2}} = {{\sqrt 5 + (\sqrt 3 - 2)} \over {\left[ {\sqrt 5 - (\sqrt 3 - 2)} \right]\left[ {\sqrt 5 + (\sqrt 3 - 2)} \right]}}\)
\( = {{\sqrt 5 + (\sqrt 3 - 2)} \over {5 - {{(\sqrt 3 - 2)}^2}}} = {{\sqrt 5 + (\sqrt 3 - 2)} \over {5 - (3 - 4\sqrt 3 + 4)}} = {{\sqrt 5 + (\sqrt 3 - 2)} \over {4\sqrt 3 - 2}}\)
\(= {{\sqrt 5 + \sqrt 3 - 2} \over {2(2\sqrt 3 - 1)}} = {{(\sqrt 5 + \sqrt 3 - 2)(2\sqrt 3 + 1)} \over {2\left[ {(2\sqrt 3 - 1)(2\sqrt 3 + 1)} \right]}}\)
\(\eqalign{
& = {{2\sqrt {15} + \sqrt 5 + 6 + \sqrt 3 - 4\sqrt 3 - 2} \over {2(12 - 1)}} \cr
& = {{2\sqrt {15} + \sqrt 5 + 4 - 3\sqrt 3 } \over {22}} \cr} \)