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Omni-MATH / Let a,b,c be non-negative real numbers such that ab+bc+ca=3. Suppose that a³b+b³c+c³a+2abc(a+b+c)=(9)/(2). What is the minimum possible value of ab³+bc³+ca³?

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problem

Let a,b,ca, b, c be non-negative real numbers such that ab+bc+ca=3ab+bc+ca=3. Suppose that a3b+b3c+c3a+2abc(a+b+c)=92a^{3}b+b^{3}c+c^{3}a+2abc(a+b+c)=\frac{9}{2}. What is the minimum possible value of ab3+bc3+ca3ab^{3}+bc^{3}+ca^{3}?
Plain-text mathematical notation (without MathML)
Let a,b,c be non-negative real numbers such that ab+bc+ca=3. Suppose that a³b+b³c+c³a+2abc(a+b+c)=(9)/(2). What is the minimum possible value of ab³+bc³+ca³?
Original LaTeX notation
Let $a, b, c$ be non-negative real numbers such that $ab+bc+ca=3$. Suppose that $a^{3}b+b^{3}c+c^{3}a+2abc(a+b+c)=\frac{9}{2}$. What is the minimum possible value of $ab^{3}+bc^{3}+ca^{3}$?

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Source and history

task_id
9996d188-f7c3-5047-82c0-d3627622e307
task_key
test--9996d188-f7c3-5047-82c0-d3627622e307
task_revision_id
1
config / split
/ test

Official source

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