Thực hiện phép tính \(B = \left( {\frac{{\sqrt {14} - \sqrt 7 }}{{1 - \sqrt 2 }} + \frac{{\sqrt {15} - \sqrt 5 }}{{1 - \sqrt 3 }}} \right):\frac{1}{{\sqrt 7 - \sqrt 5 }}\).

8/12

−2.

\({\left( {\sqrt 7 - \sqrt 5 } \right)^2}\).

Giải thích

Đáp án đúng là: B

\(B = \left( {\frac{{\sqrt {14} - \sqrt 7 }}{{1 - \sqrt 2 }} + \frac{{\sqrt {15} - \sqrt 5 }}{{1 - \sqrt 3 }}} \right):\frac{1}{{\sqrt 7 - \sqrt 5 }}\)

\(B = \left[ {\frac{{\left( {\sqrt {14} - \sqrt 7 } \right)\left( {1 - \sqrt 3 } \right) + \left( {\sqrt {15} - \sqrt 5 } \right)\left( {1 - \sqrt 2 } \right)}}{{\left( {1 - \sqrt 2 } \right)\left( {1 - \sqrt 3 } \right)}}} \right].\left( {\sqrt 7 - \sqrt 5 } \right)\)

\(B = \left[ {\frac{{\left( {\sqrt {14} - \sqrt 7 } \right)\left( {1 - \sqrt 3 } \right) + \sqrt 5 \left( {\sqrt 3 - 1} \right)\left( {1 - \sqrt 2 } \right)}}{{\left( {1 - \sqrt 2 } \right)\left( {1 - \sqrt 3 } \right)}}} \right].\left( {\sqrt 7 - \sqrt 5 } \right)\)

\(B = \left[ {\frac{{\left( {\sqrt {14} - \sqrt 7 - \sqrt 5 + \sqrt {10} } \right)\left( {1 - \sqrt 3 } \right)}}{{\left( {1 - \sqrt 2 } \right)\left( {1 - \sqrt 3 } \right)}}} \right].\left( {\sqrt 7 - \sqrt 5 } \right)\)

\(B = \frac{{\left( {\sqrt 7 + \sqrt 5 } \right)\left( {\sqrt 2 - 1} \right)\left( {1 - \sqrt 3 } \right)}}{{\left( {1 - \sqrt 2 } \right)\left( {1 - \sqrt 3 } \right)}}.\left( {\sqrt 7 - \sqrt 5 } \right)\)

\(B = - \left( {\sqrt 7 - \sqrt 5 } \right)\left( {\sqrt 7 + \sqrt 5 } \right) = - \left( {7 - 5} \right) = - 2\).