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Excel in math and science
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Algebraic Manipulation
Gauss, Ramanujan, and a pantheon of other mathematicians have given us algebraic manipulation tools way beyond what's taught in school. Learn what they knew.
Excel in math and science
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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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Concept Quizzes
If \(a\) and \(b\) are real numbers such that \[a^2+b^2=8, ab=3,\] what is the value of \[\frac{a^7-ab^6-ba^6+b^7}{a+b}?\]
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 that \(x\) and \(y\) are positive real numbers satisfying \(x^2+y^2 = 5xy\). Then \( \frac{x-y}{x+y} \) can be written as \( \sqrt{\frac{a}{b}} \), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).
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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\(a\), \(b\) and \(c\) are real numbers such that \[a+b+c \neq 0, a^3+b^3+c^3=12, abc=4.\] What is the value of \((a+b)(b+c)(c+a)?\)
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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If \(A-B=-4\) and \(AB=62\), what is the value of \(A^2+B^2\)?
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
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Given \(a+b+c=4\), \(a^2+b^2+c^2=24\) and \(a^3+b^3+c^3=6,\) what is the value of \[ab(a+b)+bc(b+c)+ca(c+a)?\]
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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by Brilliant Staff