Question Number 164966 by Zaynal last updated on 24/Jan/22
$$\:\:\:\:\:\lfloor\left(\frac{\mathrm{5}}{\boldsymbol{{x}}}\:+\:\frac{\mathrm{4}}{\boldsymbol{{x}}}\:+\:\frac{\mathrm{3}}{\boldsymbol{{x}}}\:+\:\frac{\mathrm{2}}{\boldsymbol{{x}}}\:+\:\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)\:\bullet\:\left(\frac{\boldsymbol{{x}}}{\mathrm{1}}\:−\:\frac{\boldsymbol{{x}}}{\mathrm{2}}\:−\:\frac{\boldsymbol{{x}}}{\mathrm{3}}\:\:−\:\frac{\boldsymbol{{x}}}{\mathrm{4}}\:−\:\frac{\boldsymbol{{x}}}{\mathrm{5}}\:\right)^{\mathrm{2}} >\:\frac{\mathrm{1}}{\mathrm{15}}\rfloor \\ $$$$\:\:\:\left\{\mathrm{za}\right\} \\ $$
Answered by alephzero last updated on 24/Jan/22
$$\frac{\mathrm{15}}{{x}}\:×\:\frac{\mathrm{17}^{\mathrm{2}} {x}^{\mathrm{2}} }{\mathrm{60}^{\mathrm{2}} }\:>\:\frac{\mathrm{1}}{\mathrm{15}} \\ $$$$\frac{\mathrm{289}{x}}{\mathrm{240}}\:>\:\frac{\mathrm{1}}{\mathrm{15}} \\ $$$$\Rightarrow\:{x}\:>\:\frac{\mathrm{16}}{\mathrm{289}} \\ $$