a) ( √6+27)( √3- √2)
b)( √3+1) ²-2 √3+4
e) (1+2 √3- √2)(1+2 √3+ √2)
c) (1+ √2- √3)(1+ √2+3)
d) √3( √2- √3) ²-( √3+ √2)
g(1- √3) ²(1+2 √3) ²
a) ( √6+27)( √3- √2)
b)( √3+1) ²-2 √3+4
e) (1+2 √3- √2)(1+2 √3+ √2)
c) (1+ √2- √3)(1+ √2+3)
d) √3( √2- √3) ²-( √3+ √2)
g(1- √3) ²(1+2 √3) ²
Giải thích các bước giải:
\(\begin{array}{l}
a,\\
\left( {\sqrt 6 + 27} \right)\left( {\sqrt 3 – \sqrt 2 } \right)\\
= \sqrt 6 .\sqrt 3 – \sqrt 6 .\sqrt 2 + 27.\sqrt 3 – 27\sqrt 2 \\
= \sqrt 3 .\sqrt 2 .\sqrt 3 – \sqrt 3 .\sqrt 2 .\sqrt 2 + 27\sqrt 3 – 27\sqrt 2 \\
= 3\sqrt 2 – 2\sqrt 3 + 27\sqrt 3 – 27\sqrt 2 \\
= – 24\sqrt 2 + 25\sqrt 3 \\
b,\\
{\left( {\sqrt 3 + 1} \right)^2} – 2\sqrt 3 + 4\\
= \left( {3 + 2\sqrt 3 + 1} \right) – 2\sqrt 3 + 4\\
= \left( {4 + 2\sqrt 3 } \right) – 2\sqrt 3 + 4\\
= 8\\
c,\\
\left( {1 + \sqrt 2 – \sqrt 3 } \right)\left( {1 + \sqrt 2 + \sqrt 3 } \right)\\
= \left[ {\left( {1 + \sqrt 2 } \right) – \sqrt 3 } \right]\left[ {\left( {1 + \sqrt 2 } \right) + \sqrt 3 } \right]\\
= {\left( {1 + \sqrt 2 } \right)^2} – {\sqrt 3 ^2}\\
= \left( {1 + 2\sqrt 2 + 2} \right) – 3\\
= 2\sqrt 2 \\
d,\\
\sqrt 3 {\left( {\sqrt 2 – \sqrt 3 } \right)^2} – \left( {\sqrt 3 + \sqrt 2 } \right)\\
= \sqrt 3 .\left( {2 – 2\sqrt 2 .\sqrt 3 + 3} \right) – \left( {\sqrt 3 + \sqrt 2 } \right)\\
= \sqrt 3 .\left( {5 – 2\sqrt 2 .\sqrt 3 } \right) – \sqrt 3 – \sqrt 2 \\
= 5\sqrt 3 – 2\sqrt 2 .{\sqrt 3 ^2} – \sqrt 3 – \sqrt 2 \\
= 5\sqrt 3 – 6\sqrt 2 – \sqrt 3 – \sqrt 2 \\
= 4\sqrt 3 – 7\sqrt 2 \\
e,\\
\left( {1 + 2\sqrt 3 – \sqrt 2 } \right).\left( {1 + 2\sqrt 3 + \sqrt 2 } \right)\\
= \left[ {\left( {1 + 2\sqrt 3 } \right) – \sqrt 2 } \right].\left[ {\left( {1 + 2\sqrt 3 } \right) + \sqrt 2 } \right]\\
= {\left( {1 + 2\sqrt 3 } \right)^2} – {\sqrt 2 ^2}\\
= \left( {1 + 4\sqrt 3 + 12} \right) – 2\\
= 11 + 4\sqrt 3 \\
g,\\
{\left( {1 – \sqrt 3 } \right)^2}{\left( {1 + 2\sqrt 3 } \right)^2}\\
= \left( {1 – 2\sqrt 3 + 3} \right).\left( {1 + 4\sqrt 3 + 12} \right)\\
= \left( {4 – 2\sqrt 3 } \right)\left( {13 + 4\sqrt 3 } \right)\\
= 52 + 16\sqrt 3 – 26\sqrt 3 – 24\\
= 28 – 10\sqrt 3
\end{array}\)
Đáp án:
Giải thích các bước giải: