a) $\sqrt{7 – 4\sqrt{3}}$ + $\sqrt{7 +4\sqrt{3} }$
b) $\sqrt{23}$ + 8$\sqrt{7}$ – $\sqrt{7}$
c) $\sqrt{11}$ – 6$\sqrt{2}$ – 3 + $\sqrt{2}$
d) $\sqrt{x^{2} -12x +36-x}$
e) $\sqrt{x-1-2\sqrt{x-2}}$ + $\sqrt{x-1+2\sqrt{x-2}}$
Giúp mình với vote 5 sao cảm ơn câu trl hay nhất đầy đủ
Đáp án:
$\begin{array}{l}
a)\sqrt {7 – 4\sqrt 3 } + \sqrt {7 + 4\sqrt 3 } \\
= \sqrt {{{\left( {2 – \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} \\
= 2 – \sqrt 3 + 2 + \sqrt 3 \\
= 4\\
b)\sqrt {23 + 8\sqrt 7 } – \sqrt 7 \\
= \sqrt {16 + 2.4.\sqrt 7 + 7} – \sqrt 7 \\
= \sqrt {{{\left( {4 + \sqrt 7 } \right)}^2}} – \sqrt 7 \\
= 4 + \sqrt 7 – \sqrt 7 \\
= 4\\
c)\sqrt {11 – 6\sqrt 2 } – 3 + \sqrt 2 \\
= \sqrt {9 – 2.3.\sqrt 2 + 2} – 3 + \sqrt 2 \\
= \sqrt {{{\left( {3 – \sqrt 2 } \right)}^2}} – 3 + \sqrt 2 \\
= 3 – \sqrt 2 – 3 + \sqrt 2 \\
= 0\\
d)\sqrt {{x^2} – 12x + 36} – x\\
= \sqrt {{{\left( {x – 6} \right)}^2}} – x\\
= \left| {x – 6} \right| – x\\
\left[ \begin{array}{l}
= x – 6 – x = – 6\left( {khi:x \ge 6} \right)\\
= 6 – x – x = 6 – 2x\left( {khi:x < 6} \right)
\end{array} \right.\\
e)\sqrt {x – 1 – 2\sqrt {x – 2} } + \sqrt {x – 1 + 2\sqrt {x – 2} } \\
= \sqrt {x – 2 – 2\sqrt {x – 2} + 1} \\
+ \sqrt {x – 2 + 2\sqrt {x – 2} + 1} \\
= \sqrt {{{\left( {\sqrt {x – 2} – 1} \right)}^2}} + \sqrt {{{\left( {\sqrt {x – 2} + 1} \right)}^2}} \\
= \left| {\sqrt {x – 2} – 1} \right| + \sqrt {x – 2} + 1\\
= \left[ \begin{array}{l}
\sqrt {x – 2} – 1 + \sqrt {x – 2} + 1\left( {khi:x \ge 3} \right)\\
1 – \sqrt {x – 2} + \sqrt {x – 2} + 1\left( {khi:x < 3} \right)
\end{array} \right.\\
= \left[ \begin{array}{l}
2\sqrt {x – 2} \left( {khi:x \ge 3} \right)\\
2\left( {khi:x < 3} \right)
\end{array} \right.
\end{array}$