hint:Albert said:$x,y,z>1$
please prove :
$\dfrac{x^4}{(y-1)^2}+\dfrac{y^4}{(z-1)^2}+\dfrac{z^4}{(x-1)^2}\geq 48$
Albert said:hint:
prove :$\dfrac{x^4}{(y-1)^2}\geq 32(x-y)+16$
"Proof of an inequality" is a technique used in mathematics to show that one mathematical expression is less than or greater than another. It is commonly used to compare the sizes of two quantities or to show that one quantity is always smaller or larger than another.
"Proof of an inequality" is important because it allows us to make precise comparisons between quantities and to establish relationships between them. This is crucial in many fields of science, such as physics, economics, and engineering, where accurate and rigorous analysis is essential.
The proof of an inequality involves using mathematical principles and logical reasoning to show that one expression is always greater than or less than another. This can be achieved through various methods, such as algebraic manipulation, calculus, or mathematical induction.
The key elements of a "Proof of an inequality" include clearly stating the inequality to be proved, providing a logical and rigorous argument, and using appropriate mathematical techniques and principles. It is also important to clearly define any variables or terms used in the proof.
Yes, "Proof of an inequality" has many practical applications in fields such as economics, physics, and engineering. It can be used to analyze and compare data, make predictions, and solve real-world problems involving quantities and their relationships.