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Category: Algebra

Find-the-minimum-of-12-x-18-y-xy-for-all-positive-number-x-amp-y-

Question Number 141135 by bobhans last updated on 16/May/21 $$\:\:\:\:\:\:\:{Find}\:{the}\:{minimum}\:{of}\: \\ $$$$\:\:\:\:\:\:\frac{\mathrm{12}}{{x}}\:+\:\frac{\mathrm{18}}{{y}}\:+\:{xy}\:{for}\:{all}\: \\ $$$$\:\:\:\:\:\:{positive}\:{number}\:{x}\:\&\:{y}\:. \\ $$ Answered by mitica last updated on 16/May/21 $$\frac{\mathrm{12}}{{x}}+\frac{\mathrm{18}}{{y}}+{xy}\geqslant\mathrm{3}\sqrt[{\mathrm{3}}]{\frac{\mathrm{12}}{{x}}\centerdot\frac{\mathrm{18}}{{y}}\centerdot{xy}}=\mathrm{18} \\…

x-3-x-2-9-1-x-

Question Number 10043 by konen last updated on 21/Jan/17 $$\mid\mathrm{x}−\mathrm{3}\mid^{\mathrm{x}^{\mathrm{2}} −\mathrm{9}} =\mathrm{1}\:\:\Rightarrow\Sigma\mathrm{x}=? \\ $$ Answered by mrW1 last updated on 22/Jan/17 $${if}\:{a}^{{b}} =\mathrm{1},\:{then} \\ $$$${a}=\mathrm{1}\:{or}…

Show-that-log-10-x-1-give-the-number-of-digits-for-x-Z-

Question Number 10040 by FilupSmith last updated on 21/Jan/17 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\lfloor\mathrm{log}_{\mathrm{10}} \left({x}\right)+\mathrm{1}\rfloor\:\:\:\mathrm{give}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{digits}\:\mathrm{for}\:{x}\in\mathbb{Z} \\ $$ Answered by mrW1 last updated on 21/Jan/17 $${let}\:{x}\:{be}\:{an}\:{integer}\:{with}\:{n}\:{digits},\:{then}…