Đáp án:
1
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{\sqrt {12 - 2\sqrt {35} } + \sqrt {6 - 2\sqrt 5 } }}{{\sqrt {8 + 2\sqrt 7 } }}\\
= \dfrac{{\sqrt {7 - 2.\sqrt 7 .\sqrt 5 + 5} + \sqrt {5 - 2\sqrt 5 .1 + 1} }}{{\sqrt {7 + 2\sqrt 7 .1 + 1} }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 7 - \sqrt 5 } \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} }}{{\sqrt {{{\left( {\sqrt 7 + 1} \right)}^2}} }}\\
= \dfrac{{\sqrt 7 - \sqrt 5 + \sqrt 5 - 1}}{{\sqrt 7 + 1}}\\
= \dfrac{{\sqrt 7 - 1}}{{\sqrt 7 + 1}} = \dfrac{{{{\left( {\sqrt 7 - 1} \right)}^2}}}{{\left( {\sqrt 7 + 1} \right)\left( {\sqrt 7 - 1} \right)}}\\
= \dfrac{{8 - 2\sqrt 7 }}{{7 - 1}} = \dfrac{{8 - 2\sqrt 7 }}{6}\\
= \dfrac{4}{3} - \dfrac{{\sqrt 7 }}{3}\\
\to a = \dfrac{4}{3};b = - \dfrac{1}{3}\\
\to a + b = \dfrac{4}{3} - \dfrac{1}{3} = 1
\end{array}\)
