Appoint all the pairs (k, l) (both k and l in R^+) such that:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sqrt{k}+\sqrt{l}=\sqrt{4+\sqrt{7}}[/tex]

I'm really stuck at it. First of all, I think that getting rid of the roots may be a good idea so we have:

[tex]k+l+2\sqrt{kl}=4+\sqrt{7}[/tex]

[tex]2\sqrt{k \ell}-\sqrt{7}=4-k-\ell[/tex]

[tex]7+4 k \ell-4 \sqrt{7} \sqrt{k \ell}=16-8 k+k^2-8 \ell+2 k \ell+\ell^2[/tex]

...but when we get to the equation with no roots left at all (I mean, when [tex]-4\sqrt{7kl}[/tex] turns into 112kl), it's REALLY long (and by "REALLY" I mean around 90 characters long). Does it sound right or not really?

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# Appoint all the pairs

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