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Omni-MATH / Let a,b,c be positive real numbers such that abc=(1)/(8). Prove the inequality:a²+b²+c²+a²b²+b²c²+c²a²≥(15)/(16) When the equality holds?

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problem

Let a,b,ca, b, c be positive real numbers such that abc=18abc = \dfrac {1} {8}. Prove the inequality:a2+b2+c2+a2b2+b2c2+c2a2≥1516a ^ 2 + b ^ 2 + c ^ 2 + a ^ 2b ^ 2 + b ^ 2c ^ 2 + c ^ 2a ^ 2 \geq \dfrac {15} {16} When the equality holds?
Plain-text mathematical notation (without MathML)
Let a,b,c be  positive real numbers such that abc=(1)/(8). Prove the inequality:a²+b²+c²+a²b²+b²c²+c²a²≥(15)/(16)
When the equality holds?
Original LaTeX notation
Let $a, b, c$ be  positive real numbers such that $abc = \dfrac {1} {8}$. Prove the inequality:$$a ^ 2 + b ^ 2 + c ^ 2 + a ^ 2b ^ 2 + b ^ 2c ^ 2 + c ^ 2a ^ 2 \geq \dfrac {15} {16}$$
When the equality holds?

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Source and history

task_id
4de6e25e-9e1f-557c-8038-69ca77655b05
task_key
test--4de6e25e-9e1f-557c-8038-69ca77655b05
task_revision_id
1
config / split
/ test

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