Toán Lớp 9: tính A=√(4-√7)-√(4+√7) và B=11*∛(5-√17)*∛(5+√17)
ai đúng mình vote 5 sao
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Toán Lớp 9: tính A=√(4-√7)-√(4+√7) và B=11*∛(5-√17)*∛(5+√17)
ai đúng mình vote 5 sao
Comments ( 1 )
A = \sqrt {4 – \sqrt 7 } – \sqrt {4 + \sqrt 7 } \\
\Rightarrow A\sqrt 2 = \sqrt {8 – 2\sqrt 7 } – \sqrt {8 + 2\sqrt 7 } \\
\Rightarrow A\sqrt 2 = \sqrt {{{\left( {\sqrt 7 – 1} \right)}^2}} – \sqrt {{{\left( {\sqrt 7 + 1} \right)}^2}} \\
\Rightarrow A\sqrt 2 = \sqrt 7 – 1 – \sqrt 7 – 1 = – 2\\
\Rightarrow A = – \sqrt 2 \\
B = 11\sqrt[3]{{5 – \sqrt {17} }}.\sqrt[3]{{5 + \sqrt {17} }}\\
B = 11\sqrt[3]{{\left( {5 – \sqrt {17} } \right)\left( {5 + \sqrt {17} } \right)}} = 11\sqrt[3]{{25 – 17}} = 11.2\\
B = 22
\end{array}$