tính giá trị biểu thức
1.√(x-2-2√(x-3)) √(x+1-4√(x-3))
2. (4√3 -4) √(3+√(5- √(13+2√12)))
3. √(0,25√961+2√10 + √15 + √6)
tính giá trị biểu thức
1.√(x-2-2√(x-3)) √(x+1-4√(x-3))
2. (4√3 -4) √(3+√(5- √(13+2√12)))
3. √(0,25√961+2√10 + √15 + √6)
Đáp án:
$\begin{array}{l}
1)\sqrt {x – 2 – 2\sqrt {x – 3} } .\sqrt {x + 1 – 4\sqrt {x – 3} } \\
= \sqrt {x – 3 – 2.\sqrt {x – 3} + 1} .\\
\sqrt {x – 3 – 4\sqrt {x – 3} + 4} \\
= \sqrt {{{\left( {\sqrt {x – 3} – 1} \right)}^2}} .\sqrt {{{\left( {\sqrt {x – 3} – 2} \right)}^2}} \\
= \left| {\sqrt {x – 3} – 1} \right|.\left| {\sqrt {x – 3} – 2} \right|\\
= \left| {x – 3 – 3\sqrt {x – 3} + 2} \right|\\
= \left| {x – 1 – 3\sqrt {x – 3} } \right|\\
2)\left( {4\sqrt 3 – 4} \right).\sqrt {3 + \sqrt {5 – \sqrt {13 + 2\sqrt {12} } } } \\
= 4.\left( {\sqrt 3 – 1} \right).\sqrt {3 + \sqrt {5 – \sqrt {{{\left( {\sqrt {12} + 1} \right)}^2}} } } \\
= 4\left( {\sqrt 3 – 1} \right).\sqrt {3 + \sqrt {5 – \sqrt {12} – 1} } \\
= 4\left( {\sqrt 3 – 1} \right).\sqrt {3 + \sqrt {4 – 2\sqrt 3 } } \\
= 4\left( {\sqrt 3 – 1} \right).\sqrt {3 + \sqrt {{{\left( {\sqrt 3 – 1} \right)}^2}} } \\
= 4\left( {\sqrt 3 – 1} \right).\sqrt {3 + \sqrt 3 – 1} \\
= 4\left( {\sqrt 3 – 1} \right).\sqrt {2 + \sqrt 3 } \\
= 2\sqrt 2 .\left( {\sqrt 3 – 1} \right).\sqrt 2 .\sqrt {2 + \sqrt 3 } \\
= 2\sqrt 2 \left( {\sqrt 3 – 1} \right).\sqrt {4 + 2\sqrt 3 } \\
= 2\sqrt 2 .\left( {\sqrt 3 – 1} \right).\sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} \\
= 2\sqrt 2 \left( {\sqrt 3 – 1} \right).\left( {\sqrt 3 + 1} \right)\\
= 2\sqrt 2 \left( {3 – 1} \right)\\
= 2\sqrt 2 .2\\
= 4\sqrt 2 \\
3)\sqrt {0,25\sqrt {961} + 2\sqrt {10} + \sqrt {15} + \sqrt 6 }
\end{array}$