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anemone
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If $a$ and $b$ are two positive real, and that $a^3+b^3=a-b$, prove that $2\left(\sqrt{2}-1\right)a^2-b^2\lt 1$.
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it should be:If $a$ and $b$ are two positive real, and that $a^3+b^3=a-b$, prove that $2\left(\sqrt{2}-1\right)a^2-b^2<1$.anemone said:If $a$ and $b$ are two positive real, and that $a^3+b^3=a-b$, prove that $2\left(\sqrt{2}-1\right)a^2-b^2\le 1$.
anemone said:If $a$ and $b$ are two positive real, and that $a^3+b^3=a-b$, prove that $2\left(\sqrt{2}-1\right)a^2-b^2\le 1$.
The inequality challenge for positive real numbers is a mathematical problem that involves finding the minimum and maximum values of a set of positive real numbers, while also satisfying a given inequality. This challenge is often used in mathematical competitions and can also have practical applications in economics and finance.
To solve an inequality challenge for positive real numbers, you must first understand the given inequality and the set of positive real numbers. Then, you can use various methods such as algebraic manipulation, graphing, or using calculus techniques to find the minimum and maximum values that satisfy the inequality.
The inequality challenge for positive real numbers is important as it tests a person's ability to think critically and creatively to solve a mathematical problem. It also has practical applications in fields such as economics and finance, where finding the minimum and maximum values of a set of positive real numbers can help make informed decisions.
Some strategies for solving an inequality challenge for positive real numbers include understanding the properties of inequalities, using trial and error, and breaking down the problem into smaller parts. Additionally, using graphical representations or utilizing mathematical software can also be helpful in finding solutions.
Yes, some tips for approaching an inequality challenge for positive real numbers include carefully reading and understanding the given problem, identifying any patterns or relationships between the numbers, and using multiple methods to solve the challenge. It is also important to check your solutions and make sure they satisfy the given inequality.