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Question 9 : If x = (4096)7+4√3, then which of the following equals 64?

  1. \\frac{x^{7/2}}{x^{4/√3}})
  2. \\frac{x^{7}}{x^{4√3}})
  3. \\frac{x^{7/2}}{x^{2√3}})
  4. \\frac{x^{7}}{x^{2√3}})

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Explanatory Answer

642 = 4096
x = (4096)7 + 4√3
x = (642)7 + 4√3
√x = (64)7 + 4√3
√x( 1 ÷ (7 + 4√3)) = 64

1 ÷ (7 + 4√3) = \\frac{1}{7 + 4√3}) = \\frac{1 × (7 - 4√3)}{(7 + 4√3) × (7 - 4√3)}) = \\frac{7 - 4√3}{49 - 48}) = 7 - 4√3

√x( 1 ÷ (7 + 4√3)) = 64
√x(7 - 4√3) = 64
x(7/2 - (4√3)/2) = 64
x(7/2 - 2√3) = 64
\\frac{x^{7/2}}{x^{2√3}})


The question is "If x = (4096)7+4√3, then which of the following equals 64?"

Hence, the answer is, "\\frac{x^{7/2}}{x^{2√3}})"

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