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Home » Question: Rationalize the denominator of $ \frac5\sqrt7 + \sqrt2 $. - Nelissen Grade advocaten

Question: Rationalize the denominator of $ \frac5\sqrt7 + \sqrt2 $. - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 = 2 \times 66 = 2 \times 2 \times 33 = 2^2 \times 3 \times 11

📌 The distinct prime factors are 2, 3, and 11. Summing them:

📌 + 3 + 11 = 16

📌 Thus, the sum of the distinct prime factors is $\boxed{16}$.

📌 Question: For how many integer values of $x$ does the equation $\sqrt{(x - 7)^2} = 9$ hold true?

📌 Solution: Recall that $\

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Substitute \(x = 2\):
f'(2) = 3(2)^2 - 8(2) + 5 = 12 - 16 + 5 = 1
Solve the logarithmic equation \(\log_2(x+3) + \log_2(x-1) = 3\).
Combine logs:
\log_2[(x+3)(x-1)] = 3
Convert to exponential form:
Expand and solve:
x^2 + 2x - 3 = 8
x^2 + 2x - 11 = 0
x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2}

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