## Rút gọn: a) A= √(1-√3)^2 – √(√3+2)^2 b) B= √(2-√3)^2 – √4-2√3 c) C= √15-6√6 + √33-12√6 d) D= √2-√3 – √2+√3

Question

Rút gọn:
a) A= √(1-√3)^2 – √(√3+2)^2
b) B= √(2-√3)^2 – √4-2√3
c) C= √15-6√6 + √33-12√6
d) D= √2-√3 – √2+√3

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1 year 2020-10-31T23:33:11+00:00 1 Answers 164 views 0

$$D = – \sqrt 2$$
$$\begin{array}{l} \sqrt {{{\left( {1 – \sqrt 3 } \right)}^2}} – \sqrt {{{\left( {\sqrt 3 + 2} \right)}^2}} \\ = \left| {1 – \sqrt 3 } \right| – \left| {\sqrt 3 + 2} \right|\\ = \sqrt 3 – 1 – \left( { – \sqrt 3 – 2} \right)\left( {do:1 < \sqrt 3 < 2} \right)\\ = \sqrt 3 – 1 + \sqrt 3 + 2\\ = 2\sqrt 3 + 1\\ b.B = \sqrt {{{\left( {2 – \sqrt 3 } \right)}^2}} – \sqrt {4 – 2\sqrt 3 } \\ = 2 – \sqrt 3 – \sqrt {3 – 2\sqrt 3 .1 + 1} \\ = 2 – \sqrt 3 – \sqrt {{{\left( {\sqrt 3 – 1} \right)}^2}} \\ = 2 – \sqrt 3 – \sqrt 3 + 1\\ = 3 – 2\sqrt 3 \\ c.C = \sqrt {15 – 6\sqrt 6 } + \sqrt {33 – 12\sqrt 6 } \\ = \sqrt {9 – 2.3.\sqrt 6 + 6} + \sqrt {24 – 2.2\sqrt 6 + 9} \\ = \sqrt {{{\left( {3 – \sqrt 6 } \right)}^2}} + \sqrt {{{\left( {2\sqrt 6 – 3} \right)}^2}} \\ = 3 – \sqrt 6 + 2\sqrt 6 – 3 = \sqrt 6 \\ d.D = \sqrt {2 – \sqrt 3 } – \sqrt {2 + \sqrt 3 } \\ = \dfrac{{\sqrt {4 – 2\sqrt 3 } – \sqrt {4 + 2\sqrt 3 } }}{{\sqrt 2 }}\\ = \dfrac{{\sqrt {3 – 2\sqrt 3 .1 + 1} – \sqrt {3 + 2\sqrt 3 .1 + 1} }}{{\sqrt 2 }}\\ = \dfrac{{\sqrt {{{\left( {\sqrt 3 – 1} \right)}^2}} – \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} }}{{\sqrt 2 }}\\ = \dfrac{{\sqrt 3 – 1 – \sqrt 3 – 1}}{{\sqrt 2 }}\\ = \dfrac{{ – 2}}{{\sqrt 2 }} = – \sqrt 2 \end{array}$$