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2936131
03.06.2021 •
Mathematics
K is a prime number and f(x) = k has no solutions.
Find the possible values of k.
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Ответ:
Suppose x∈R is such that x+20x=p is a prime. Then x2−px+20=0 , and this equation has a solution x∈R if and only if p2–80≥0 . So the primes which admit no real solution are those that satisfy p<80−−√ , or 2 , 3 , 5 , and 7 . ■
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