CAT 2020 Question Paper | Quants Slot 1

CAT Questions

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

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Video Explanation

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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}})

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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}})"