IMO LONGLISTED PROBLEM 1970

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MATHPRITOM
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IMO LONGLISTED PROBLEM 1970

Unread post by MATHPRITOM » Sun May 01, 2011 1:27 pm

Show the equation $\sqrt{2-x^{2}}+\sqrt{3-x^{3}}=0$ has no real roots.

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Moon
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Re: IMO LONGLISTED PROBLEM 1970

Unread post by Moon » Fri May 20, 2011 12:20 am

Because both of them must be non-negative i.e. zero.

BTW older IMO (and IMO shortlist) problems are quite irrelevant to the current IMO problems. So it is advisable that you start from the problems of the 90s.
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Tahmid Hasan
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Re: IMO LONGLISTED PROBLEM 1970

Unread post by Tahmid Hasan » Fri May 20, 2011 9:17 pm

i guess that involved the cubic root of the second expression of this problem
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