Toán $\sqrt[]{12+\sqrt[]{48}-\sqrt[]{60}+\sqrt[]{80}}$- $\sqrt[]{8+\sqrt[]{60}}$ 18/09/2021 By Caroline $\sqrt[]{12+\sqrt[]{48}-\sqrt[]{60}+\sqrt[]{80}}$- $\sqrt[]{8+\sqrt[]{60}}$
Đáp án: =√5+√3+2−√5−√3=2.12+48+60+80−8+60=12+43+215+45−8+215=8+215+4+43−45−5+25.3+3=5+2.5.3+3+4(3+5)+4−(5+3)2=(5+3)2+4(3+5)+4−|5+3|=(5+3+2)2−(5+3)=5+3+2−5−3=2. Giải thích các bước giải: Trả lời
\[\begin{array}{l} \sqrt {12 + \sqrt {48} + \sqrt {60} + \sqrt {80} } – \sqrt {8 + \sqrt {60} } \\ = \sqrt {12 + 4\sqrt 3 + 2\sqrt {15} + 4\sqrt 5 } – \sqrt {8 + 2\sqrt {15} } \\ = \sqrt {8 + 2\sqrt {15} + 4 + 4\sqrt 3 – 4\sqrt 5 } – \sqrt {5 + 2\sqrt 5 .\sqrt 3 + 3} \\ = \sqrt {5 + 2.\sqrt 5 .\sqrt 3 + 3 + 4\left( {\sqrt 3 + \sqrt 5 } \right) + 4} – \sqrt {{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2}} \\ = \sqrt {{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2} + 4\left( {\sqrt 3 + \sqrt 5 } \right) + 4} – \left| {\sqrt 5 + \sqrt 3 } \right|\\ = \sqrt {{{\left( {\sqrt 5 + \sqrt 3 + 2} \right)}^2}} – \left( {\sqrt 5 + \sqrt 3 } \right)\\ = \sqrt 5 + \sqrt 3 + 2 – \sqrt 5 – \sqrt 3 \\ = 2. \end{array}\] Trả lời
Đáp án:
=√5+√3+2−√5−√3=2.12+48+60+80−8+60=12+43+215+45−8+215=8+215+4+43−45−5+25.3+3=5+2.5.3+3+4(3+5)+4−(5+3)2=(5+3)2+4(3+5)+4−|5+3|=(5+3+2)2−(5+3)=5+3+2−5−3=2.
Giải thích các bước giải:
\[\begin{array}{l}
\sqrt {12 + \sqrt {48} + \sqrt {60} + \sqrt {80} } – \sqrt {8 + \sqrt {60} } \\
= \sqrt {12 + 4\sqrt 3 + 2\sqrt {15} + 4\sqrt 5 } – \sqrt {8 + 2\sqrt {15} } \\
= \sqrt {8 + 2\sqrt {15} + 4 + 4\sqrt 3 – 4\sqrt 5 } – \sqrt {5 + 2\sqrt 5 .\sqrt 3 + 3} \\
= \sqrt {5 + 2.\sqrt 5 .\sqrt 3 + 3 + 4\left( {\sqrt 3 + \sqrt 5 } \right) + 4} – \sqrt {{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2}} \\
= \sqrt {{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2} + 4\left( {\sqrt 3 + \sqrt 5 } \right) + 4} – \left| {\sqrt 5 + \sqrt 3 } \right|\\
= \sqrt {{{\left( {\sqrt 5 + \sqrt 3 + 2} \right)}^2}} – \left( {\sqrt 5 + \sqrt 3 } \right)\\
= \sqrt 5 + \sqrt 3 + 2 – \sqrt 5 – \sqrt 3 \\
= 2.
\end{array}\]