Can You Find the Relationship Between a and b in This Algebra Problem?

In summary, the conversation discusses finding the relationship between two natural numbers, a and b, given that the sum of two radicals is a rational number. It is noted that if a equals b, the two radicals are equal to a+1. The conversation also mentions that a proof can be achieved by considering the given information.
  • #1
anemone
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Given that \(\displaystyle a,\,b\in\Bbb{N}\) such that \(\displaystyle \sqrt{a^2+2b+1}+\sqrt[3]{b^3+3a^2+3a+1}\) is a rational number.

Find the relationship between $a$ and $b$.
 
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  • #2
anemone said:
given that \(\displaystyle a,\,b\in N\) such that \(\displaystyle \sqrt{a^2+2b+1}+\sqrt[3]{b^3+3a^2+3a+1}\) is a rational number.

Find the relationship between $a$ and $b$.

[sp]
By inspection, we see that, if [tex]a=b[/tex], the two radicals are equal to [tex]a+1.[/tex]

[/sp]

 
  • #3
soroban said:

[sp]
By inspection, we see that, if [tex]a=b[/tex], the two radicals are equal to [tex]a+1.[/tex]

[/sp]


That's correct, soroban!(Cool)

All that's left now is its proof which can be done by applying some thought on the
square numbers and inequalities...
 

FAQ: Can You Find the Relationship Between a and b in This Algebra Problem?

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