Question Number 177932 by Spillover last updated on 11/Oct/22 $$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{c}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{c}}\:+\sqrt{\mathrm{a}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{a}}},\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P} \\ $$ Answered by Ar Brandon last updated on 11/Oct/22 $${a},\:{b},\:{c}\:\mathrm{in}\:{AP}\:\Rightarrow{b}−{a}={c}−{b}={d}\:\left(\mathrm{common}\:\mathrm{diff}\right) \\ $$$$\mathrm{If}\:{u}_{\mathrm{1}}…
Question Number 177928 by Spillover last updated on 11/Oct/22 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\left[\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}} +\mathrm{3y}}\right]\boldsymbol{\div}\left[\frac{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} −\mathrm{3xy}}{\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}} }\right]×\left[\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }\right]=\mathrm{xy} \\ $$ Answered by Ar…
Question Number 177929 by Spillover last updated on 11/Oct/22 $$\mathrm{Find}\:\mathrm{LCM}\: \\ $$$$\mathrm{3y}+\mathrm{12},\mathrm{y}^{\mathrm{2}} −\mathrm{16}\:\mathrm{and}\:\mathrm{y}^{\mathrm{4}} −\mathrm{64y} \\ $$ Answered by Ar Brandon last updated on 11/Oct/22 $$\mathrm{3y}+\mathrm{12},\:\mathrm{y}^{\mathrm{2}}…
Question Number 177931 by Spillover last updated on 11/Oct/22 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{the}\:\mathrm{principle}\:\mathrm{of}\: \\ $$$$\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}.\mathrm{4}.\mathrm{7}+\mathrm{2}.\mathrm{5}.\mathrm{8}+\mathrm{3}.\mathrm{6}.\mathrm{9}+…\mathrm{n}\left(\mathrm{n}+\mathrm{3}\right)\left(\mathrm{n}+\mathrm{6}\right) \\ $$$$=\frac{\mathrm{n}}{\mathrm{4}}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{6}\right)\left(\mathrm{n}+\mathrm{7}\right) \\ $$ Answered by Ar Brandon last updated on…
Question Number 177930 by Spillover last updated on 11/Oct/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{LCM}\: \\ $$$$\mathrm{14a}^{\mathrm{2}} \mathrm{b}^{\mathrm{3}} \mathrm{c}^{\mathrm{4}} ,\mathrm{20ab}^{\mathrm{4}} \mathrm{c}^{\mathrm{4}} \:\mathrm{and} \\ $$$$\:\mathrm{35a}^{\mathrm{5}} \mathrm{b}^{\mathrm{3}} \mathrm{c} \\ $$ Answered by…
Question Number 112360 by bemath last updated on 07/Sep/20 $$\:\:\:\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}}{\mathrm{3}}\right)^{\mathrm{3}} +\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}}{\mathrm{3}}\right)=\:\mathrm{3x}\: \\ $$ Commented by john santu last updated on 07/Sep/20 $$\frac{\left({x}^{\mathrm{3}} +{x}\right)^{\mathrm{3}}…
Question Number 177873 by mr W last updated on 10/Oct/22 $${solve}\:{for}\:{x}\in\mathbb{R} \\ $$$$\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+{x}}}}}}={x} \\ $$ Answered by Frix last updated on 10/Oct/22 $$\mathrm{for}\:\mathrm{given}\:{a}\geqslant\mathrm{0}\:\mathrm{we}\:\mathrm{need}\:{x}\:\mathrm{so}\:\mathrm{that} \\ $$$$\sqrt{{a}+{x}}={x}\:\Rightarrow\:{x}=\frac{\mathrm{1}+\sqrt{\mathrm{4}{a}+\mathrm{1}}}{\mathrm{2}}…
Question Number 177865 by Spillover last updated on 10/Oct/22 Answered by Spillover last updated on 11/Oct/22 Answered by Spillover last updated on 11/Oct/22 Terms of…
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Question Number 177866 by Spillover last updated on 10/Oct/22 Answered by Spillover last updated on 11/Oct/22 Answered by Spillover last updated on 11/Oct/22 Terms of…