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Excel in math and science
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Algebra
Power Mean Inequalities
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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Concept Quizzes
Suppose the average of \( 5 \) positive numbers is equal to \( 2. \) What is the maximum possible product of the numbers?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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by Brilliant Staff
Suppose \( xyz = 8 \) with \(x, y, z > 0. \) What is the minimum value of \( x + y + z \)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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by Brilliant Staff
What is the largest \( n \) for which
\[ x^3 + y^3 + z^3 \geq nxyz \]
holds for all \( x, y, z > 0 \)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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examples, and problems from the community.
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by Brilliant Staff
What is the largest \( n \) for which
\[ (x + y)(y + z)(x + z) \geq nxyz \]
holds for all positive \( x, y, z \)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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by Brilliant Staff
Suppose \( 2x + 3y + z = 18. \) Find the maximum value of \( xyz \) for \( x, y, z > 0. \)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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That seems reasonable.
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by Brilliant Staff