Reel Numbers

[Mohssine]

Given a and b two reel numbers such as a^5 = √2021 - √2020 et b^5= √2021 + √2020

Find the value of 1/(1+a) + 1/(1+b)

 

[Steven G]

After the number of posts you made, you know that no one here will post a solution to any math question. This is not the way this forum works. You need to show your work and then you will be given some hints.

 

[Steven G]

If you know what a^5 equals, then how do you find a? How do you find 1+a? How about 1/(1+a)?

 

[Mohssine]

If you know what a^5 equals, then how do you find a? How do you find 1+a? How about 1/(1+a)?

if i found the solution why would i come and ask it here

 

[lev888]

if i found the solution why would i come and ask it here

This forum does not provide a solution, it helps you to find one. See the difference?

 

[Dr.Peterson]

Given a and b two reel numbers such as a^5 = √2021 - √2020 et b^5= √2021 + √2020

Find the value of 1/(1+a) + 1/(1+b)

It's a very nice problem. But it's easy to find the answer using a calculator; and that answer, as I expected, is very nice and simple. The interesting part of the problem is to find a way to work it out by hand without all the calculations. That requires thinking; and I wouldn't want to take away the pleasure of discovering it.

So I'll just give a hint: I wondered if the only thing special about 2020 and 2021 might be that they differ by 1; this justifies the odd wording of "such as", which means those numbers are just an example of a general form. (I think you really just meant "such that"!)

So I changed the problem to this:

Given two real numbers a and b such that a^5 = √y - √x and b^5= √y + √x where y - x = 1, find the value of 1/(1+a) + 1/(1+b).​

Noting that the expressions for a^5 and b^5 are radical conjugates suggested something to try ...

Now have fun with it!

 

[lookagain]

It's a very nice problem.

Dr. Peterson, you are not helping here. You are being an enabler. Every time that this OP
made his thread post he did not post any
attempt with his problem. That started in February of this year. After he was corrected by
Subhotosh Khan on his first post for not showing
his work, then he should have shown an attempt
with every new thread post thereafter.

I reported his post #4 above and asked for a temporary ban on him until he starts to follow
one of the main forum rules.

Thank you to Jomo and lev888 on this matter.

 

[Deleted member 4993]

The OP has been banned for one month for not even attempting to show any work and being abrupt in answer.

 

[Steven G]

if i found the solution why would i come and ask it here

How can you not know what a^5 equals. You are told that a^5 = sqrt(2001)- sqrt(2000)!