An inequality, in need of help.

Thread starter MathematicalPhysicist
Start date Feb 6, 2006
Tags

Inequality

In summary, an inequality is a mathematical statement using symbols to compare two quantities. When an inequality is "in need of help", it means it is not in its simplest form and requires further manipulation. To help an inequality, you can use algebraic techniques and solve for the variable. The rules for solving inequalities are similar to those for equations, with the exception of reversing the inequality sign when multiplying or dividing by a negative number. Inequalities are important in science as they help us understand relationships between quantities and are essential in analyzing data and making predictions in various scientific fields.

Feb 6, 2006

MathematicalPhysicist

Gold Member

i need to prove that if x>y>0 and n>1 n natural then:
n(x-y)y^(n-1)<x^n-y^n<n(x-y)x^(n-1)

i tried almost everything from n(x^n-y^n)/x-y>(x^n-y^n)/x-y>1

but to get nothing, can someone help?

Physics news on Phys.org

Feb 6, 2006

HallsofIvy

Science Advisor

Homework Helper

You know, do you not, that xⁿ- yⁿ= (x- y)(x^n-1+ x^n-2y+ ...+ xy^n-2+ y^n-1)?

Last edited by a moderator: Feb 6, 2006

Feb 6, 2006

MathematicalPhysicist

Gold Member

well thanks.

FAQ: An inequality, in need of help.

What is an inequality?

An inequality is a mathematical statement that compares two quantities or values. It uses symbols such as <, >, ≤, or ≥ to show the relationship between the two quantities.

What does it mean for an inequality to be "in need of help"?

When an inequality is "in need of help", it means that it is not in its simplest or most organized form. It may have extraneous terms or not be properly solved, and requires further understanding or manipulation to accurately represent the relationship between the two quantities.

How can I help an inequality?

To help an inequality, you can use various algebraic techniques such as combining like terms, distributing, or factoring to simplify it. You can also solve for the variable to find the specific values that satisfy the inequality.

What are the rules for solving inequalities?

The rules for solving inequalities are similar to those for solving equations. However, when multiplying or dividing by a negative number, the direction of the inequality sign must be reversed. Additionally, if both sides of the inequality are multiplied or divided by a negative number, the direction of the inequality sign remains the same.

Why are inequalities important in science?

Inequalities are important in science as they help us represent and understand relationships between quantities, such as in equations and mathematical models. They are also essential in analyzing data and making predictions in various scientific fields such as physics, biology, and economics.