Proving ab - a - b + 2 > 1 in Simple Algebra: Tips and Hints

In summary, "proof in simple Algebra" is the process of using logical reasoning and mathematical principles to demonstrate the validity of a statement or equation in Algebra. It is important in Algebra because it allows us to verify the accuracy of our solutions and to build a strong foundation for more complex mathematical concepts. Some common strategies used in Algebraic proofs include: direct proof, proof by contradiction, induction, and proof by contrapositive. However, a proof in Algebra can be wrong if there is a mistake in the logical reasoning or if the steps used do not accurately support the statement or equation being proven. To improve skills in writing proofs in Algebra, it is important to have a strong understanding of Algebraic principles and properties, practice using different proof strategies,
  • #1
Chen
977
1
Hi,

I need to prove that for every a > 1 and b > 1 the following holds:

ab - a - b + 2 > 1

Can someone please throw me some hints? :)

Thanks,
Chen
 
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  • #2
It's equivalent to proving

ab - a - b + 1 > 0
<=>
a(b - 1) - b + 1 > 0
<=>
-a(b - 1) + b - 1 < 0
<=>
(b - 1)(1 - a) < 0.
 
  • #3
Argh, I was close but didn't see that! Thanks. :-)
 

What is "proof in simple Algebra"?

"Proof in simple Algebra" refers to the process of using logical reasoning and mathematical principles to demonstrate the validity of a statement or equation in Algebra. It involves breaking down a problem into smaller steps and using previously established rules and properties to show that the statement or equation is true.

Why is proof important in Algebra?

Proof is important in Algebra because it allows us to verify the accuracy of our solutions and to build a strong foundation for more complex mathematical concepts. It also helps us to better understand the underlying principles and relationships within Algebraic equations and systems.

What are some common strategies used in Algebraic proofs?

Some common strategies used in Algebraic proofs include: direct proof, proof by contradiction, induction, and proof by contrapositive. These strategies involve using logical reasoning, properties of numbers and equations, and mathematical operations to support and confirm the validity of a statement or equation.

Can a proof in Algebra be wrong?

Yes, a proof in Algebra can be wrong if there is a mistake in the logical reasoning or if the steps used do not accurately support the statement or equation being proven. It is important to double check and review all steps in a proof to ensure its accuracy.

How can I improve my skills in writing proofs in Algebra?

To improve your skills in writing proofs in Algebra, it is important to have a strong understanding of Algebraic principles and properties. Practice breaking down problems into smaller steps and use different proof strategies to solve them. It can also be helpful to study and analyze proofs written by others and to seek feedback from a teacher or tutor.

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