Toán Lớp 9: Tính A= √(4- √10-2√5)+√(4+ √10-2√5)
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Toán Lớp 9: Tính A= √(4- √10-2√5)+√(4+ √10-2√5)
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A = \sqrt {4 – \sqrt {10 – 2\sqrt 5 } } + \sqrt {4 + \sqrt {10 – 2\sqrt 5 } } \\
\to {A^2} = 4 – \sqrt {10 – 2\sqrt 5 } + 2\sqrt {\left( {4 – \sqrt {10 – 2\sqrt 5 } } \right)\left( {4 + \sqrt {10 – 2\sqrt 5 } } \right)} + 4 + \sqrt {10 – 2\sqrt 5 } \\
= 8 + 2\sqrt {16 – \left( {10 – 2\sqrt 5 } \right)} \\
= 8 + 2\sqrt {6 + 2\sqrt 5 } \\
= 8 + 2\sqrt {5 + 2\sqrt 5 .1 + 1} \\
= 8 + 2\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} \\
= 8 + 2\left( {\sqrt 5 + 1} \right)\\
= 10 + 2\sqrt 5 \\
\to A = \sqrt {10 + 2\sqrt 5 }
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