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Category: Arithmetic

Let-a-b-c-p-be-rational-numbers-such-that-p-is-not-a-perfect-cube-If-a-bp-1-3-cp-2-3-0-then-prove-that-a-b-c-0-

Question Number 1083 by Vishal last updated on 08/Jun/15 $${Let}\:{a},{b},{c},{p}\:{be}\:{rational}\:{numbers}\:{such}\:{that}\:{p}\:{is}\:{not}\:{a}\:{perfect}\:{cube}. \\ $$$${If}\:{a}+{bp}^{\frac{\mathrm{1}}{\mathrm{3}}} +{cp}^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{0},\:{then}\:{prove}\:{that}\:{a}={b}={c}=\mathrm{0}. \\ $$ Answered by prakash jain last updated on 08/Jun/15 $${p}^{\mathrm{1}/\mathrm{3}}…

Find-the-smallest-number-which-leaves-remainders-8-and-12-when-divided-by-28-and-32-respectively-

Question Number 1077 by Vishal last updated on 07/Jun/15 $${Find}\:{the}\:{smallest}\:{number}\:{which}\:{leaves}\:{remainders}\:\mathrm{8}\:{and}\:\mathrm{12}\: \\ $$$${when}\:{divided}\:{by}\:\mathrm{28}\:{and}\:\mathrm{32}\:{respectively}. \\ $$ Commented by prakash jain last updated on 07/Jun/15 $$\mathrm{I}\:\mathrm{assume}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{smallest}\:+\mathrm{ve}\:\mathrm{integer}. \\ $$…

8-2-

Question Number 1031 by slezthacute@Yahoo.co.id last updated on 21/May/15 $$\mathrm{8}\sqrt{\mathrm{2}} \\ $$ Answered by 123456 last updated on 21/May/15 $$\mathrm{1}<\mathrm{2}<\mathrm{4} \\ $$$$\mathrm{1}<\sqrt{\mathrm{2}}<\mathrm{2} \\ $$$$\mathrm{8}<\mathrm{8}\sqrt{\mathrm{2}}<\mathrm{16} \\…

Question-131925

Question Number 131925 by mathlove last updated on 09/Feb/21 Commented by kaivan.ahmadi last updated on 09/Feb/21 $$\mathrm{2}{x}^{\mathrm{3}} +\mathrm{24}={A} \\ $$$${x}^{\mathrm{3}} >\mathrm{24}\Rightarrow{min}\left({x}^{\mathrm{3}} \right)=\mathrm{25} \\ $$$$\Rightarrow{min}\left({A}\right)=\mathrm{2}\left(\mathrm{25}\right)+\mathrm{24}=\mathrm{74} \\…