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Question Number 18416 by Tinkutara last updated on 20/Jul/17
$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{which}\:\mathrm{satisfies} \\ $$$$\frac{\left({x}\:−\:\mathrm{5}\right)^{\mathrm{10}} \left({x}\:−\:\mathrm{13}\right)^{\mathrm{20}} \left({x}\:−\:\mathrm{19}\right)^{\mathrm{13}} }{\left({x}\:−\:\mathrm{10}\right)^{\mathrm{18}} \left({x}\:−\:\mathrm{25}\right)^{\mathrm{19}} }\:\geqslant\:\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{2}\:\leqslant\:{x}\:\leqslant\:\mathrm{30}\:\mathrm{are} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{23} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{24} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{25} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{26} \\ $$