Question about non-trivial equation

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In summary, the conversation is discussing how to write and manipulate the value of root(3)-1 in order to produce a non-trivial equation for root(3) in terms of itself. The question also asks to use this equation to show that root(3) is not rational. Hints are requested for solving the problem.
  • #1
flying2000
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Q: write roo(3)-1 in another way,and use this to produce a non-trivial equation for root(3) in terms of itself..

I don't ever know what it means?
Any hints appreciated..

thanx
 
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  • #2
flying2000 said:
Q: write roo(3)-1 in another way,and use this to produce a non-trivial equation for root(3) in terms of itself..

So [itex]\frac{1}{\sqrt{3}} = ?[/itex]

Try multiplying the top and bottom by [itex]\sqrt{3}[/itex]

Other than that, I am not sure what the question would be asking.

AM
 
  • #3
The following is the rest of the whole question..

1)write root(3)-1 in another way,and use this to produce a non-trivial equation for root(3) in terms of itself

2)suppose m,n(m,n is natural numbers) are such that m/n=root(3),use (1) to write root(3)as another combination of m and n.
3)use (2) to show that root(3) in not rational.

Any hints appreciated..

Andrew Mason said:
So [itex]\frac{1}{\sqrt{3}} = ?[/itex]

Try multiplying the top and bottom by [itex]\sqrt{3}[/itex]

Other than that, I am not sure what the question would be asking.

AM
 

1. What is a non-trivial equation?

A non-trivial equation is an equation that has at least one unknown variable and requires a non-trivial solution to find the value of that variable. In other words, it cannot be easily solved by inspection or simple manipulation.

2. How do you solve a non-trivial equation?

Solving a non-trivial equation requires using algebraic techniques such as substitution, elimination, and factoring. It may also involve using more advanced mathematical concepts such as logarithms or trigonometric functions.

3. What makes an equation non-trivial?

An equation is considered non-trivial if it has more than one unknown variable or if it requires a complex solution method. Trivial equations, on the other hand, can be solved using basic arithmetic operations.

4. Why are non-trivial equations important in science?

Non-trivial equations are important in science because they allow us to model and understand complex systems and phenomena. They are often used in physics, chemistry, and engineering to describe real-world situations and make predictions.

5. Can non-trivial equations have more than one solution?

Yes, non-trivial equations can have multiple solutions. This can happen when there are multiple values of the unknown variable that satisfy the equation. For example, a quadratic equation can have two solutions, or roots, while a cubic equation can have three solutions.

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