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Home » 20 Hidden Gems: Must-Read Alice in Wonderland Quotes Nobody Knows! - Get link 4share

20 Hidden Gems: Must-Read Alice in Wonderland Quotes Nobody Knows! - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).
Given that $ a + b + c = 0 $, substitute into the identity:
a^3 + b^3 + c^3 - 3abc = 0 \cdot (a^2 + b^2 + c^2 - ab - bc - ca) = 0.
a^3 + b^3 + c^3 = 3abc.
This completes the proof.
oxed{a^3 + b^3 + c^3 = 3abc}
Question: Compute $ \sum_{k=1}^{50} rac{1}{k(k+2)} $.
Solution: We evaluate the sum:
\sum_{k=1}^{50} rac{1}{k(k+2)}.
We use partial fractions:

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Solution: To find the average, add the two lengths and divide by 2. Fi...
3\frac{1}{4} = \frac{13}{4}, \quad 5\frac{3}{4} = \frac{23}{4}
Now, add them:
\frac{13}{4} + \frac{23}{4} = \frac{36}{4} = 9
Then divide by 2 to find the average:
\frac{9}{2} = 4.5
Thus, the average length is $\boxed{4.5}$ inches.
Question: A marine researcher is analyzing genetic sequences and disco...
Solution: Begin by factoring 132 into its prime components:
= 2 \times 66 = 2 \times 2 \times 33 = 2^2 \times 3 \times 11

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