Proving a=d: Conditional Identity

• rama
In summary, the given problem asks to prove that a = d given the equations a = 1/(1-b), b = 1/(1-c), and c = 1/(1-d). By manipulating the equations and using the given information, it can be shown that a = d. The poster also thanks another user for their help and asks for tips on writing fractions using Latex.
rama
1. The pratement, all variables and given/known data
If a =1÷(1-b) ,b=1÷(1-c),c=1÷(1-d) prove that a=d

The Attempt at a Solution

a=1÷(1-b)
a-1÷(1-b)=0
{a(1-b)-1)}÷1-b=0
a-ab-1=0
a-ab=1
similarly
b-bc=1
c-cd=1
could any of you please give a hint, this was on test for 4 marks

rama said:
1. The pratement, all variables and given/known data
If a =1÷(1-b) ,b=1÷(1-c),c=1÷(1-d) prove that a=d

The Attempt at a Solution

a=1÷(1-b)
a-1÷(1-b)=0
{a(1-b)-1)}÷1-b=0
a-ab-1=0
a-ab=1
similarly
b-bc=1
c-cd=1
could any of you please give a hint, this was on test for 4 marks

You are given
$$b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}$$
Simplify the right hand side and then use
$$a = \frac{1}{1 - b}.$$

1 person
pasmith thanks for your time I finally got it
actually I hesitated to post such easy problems (for this PF level)
good to see you taking time on helping me
by the way how do you write fractions?

Use Latex
Click on the sigma sign on the Advanced editor for references.
Use two #s around the code.
For example \frac{1}{2} and putting two #s around will give ##\frac{1}{2}##
If you want to see what others used,right click on the rendered Latex code,>Show Math as> Tex commands.
Pasmith used this Code:
b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}

1. What does it mean to prove a=d?

Proving a=d means to demonstrate that two mathematical expressions, a and d, are equal to each other. This is typically done by using logical reasoning and mathematical operations to show that both expressions are equivalent.

2. What is a conditional identity?

A conditional identity is a statement that shows a relationship between two mathematical expressions, where one expression can be transformed into the other through a set of logical steps or conditions. In the case of a=d, this means that a and d can be proven to be equal through a series of steps.

3. How do you prove a=d?

To prove a=d, you will need to use the properties of equality and basic algebraic operations to manipulate the expressions a and d until they are equal to each other. This process typically involves substituting values, simplifying expressions, and showing that both sides are equivalent.

4. Why is it important to prove a=d?

Proving a=d is important because it allows us to confidently use mathematical expressions in place of each other. By proving that two expressions are equal, we can solve equations, simplify complex expressions, and make logical conclusions with more accuracy and efficiency.

5. What are some tips for proving a=d?

Some tips for proving a=d include carefully examining the properties of equality, being organized and systematic in your approach, and using algebraic operations to manipulate the expressions. It is also helpful to check your work and make sure that both sides of the equation are equivalent at each step.

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