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anemone
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Let $a$ and $b$ be positive real numbers such that $a+b=1$. Prove that $a^ab^b+a^bb^a\le 1$.
Inequality with positive real numbers a and b refers to a mathematical statement that compares the values of two positive real numbers. It is represented by the symbol ">" (greater than) or "<" (less than). For example, 5 > 3 means that 5 is greater than 3, while 2 < 7 means that 2 is less than 7.
Inequality with positive real numbers a and b compares the values of two numbers and determines which one is greater or less than the other. Equality, on the other hand, states that two numbers are exactly the same. In other words, inequality compares values while equality compares identities.
The rules for solving inequalities with positive real numbers a and b are similar to those for solving equations. The only difference is that when multiplying or dividing both sides by a negative number, the direction of the inequality sign must be flipped. For example, if we have -2x > 8, we must divide both sides by -2 and flip the sign to get x < -4.
Inequalities with positive real numbers a and b are commonly used in real-world situations to compare quantities. For example, they can be used to determine if a person's income is greater or less than a certain amount, or if a company's profits are increasing or decreasing over time.
Yes, inequalities with positive real numbers a and b can have more than one solution. For example, in the inequality 2x < 10, x can have multiple values such as 1, 2, 3, 4, etc. as long as it is less than 5. This is because any value of x that satisfies the inequality is considered a solution.