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anemone
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Given the real numbers $a,\,b,\,c$ and $d$, prove that
$(1+ab)^2+(1+cd)^2+a^2c^2+b^2d^2\ge 1$
$(1+ab)^2+(1+cd)^2+a^2c^2+b^2d^2\ge 1$
An inequality involving a, b, c, and d is a mathematical statement that compares the values of these variables using inequality symbols such as <, >, ≤, or ≥.
To solve an inequality involving a, b, c, and d, you must isolate the variable on one side of the inequality symbol and then use the properties of inequality to determine the possible values for that variable.
There are three main types of inequalities involving a, b, c, and d: linear inequalities, quadratic inequalities, and systems of inequalities. Linear inequalities involve variables raised to the first power, quadratic inequalities involve variables raised to the second power, and systems of inequalities involve multiple inequalities with multiple variables.
Inequalities involving a, b, c, and d can be used to represent real-life situations such as income inequality, where a, b, c, and d can represent different levels of income for different individuals. They can also be used in business and economics to represent supply and demand, production costs, and profit margins.
Some common mistakes to avoid when solving inequalities involving a, b, c, and d include forgetting to switch the direction of the inequality symbol when multiplying or dividing by a negative number, not properly distributing when simplifying expressions, and not checking the solution in the original inequality to ensure it is valid.