Question Number 174131 by Engr_Jidda last updated on 25/Jul/22 Commented by Rasheed.Sindhi last updated on 26/Jul/22 $${What}'{s}\:{meaning}\:{of}\:\overline {\mathrm{2}}\:? \\ $$$${Is}\:\overline {\mathrm{2}}=−\mathrm{2}\:? \\ $$ Commented by…
Question Number 174127 by mnjuly1970 last updated on 26/Jul/22 $$ \\ $$$$\:\:\:{Q}:\:\:\:\:\:{p}\:,\:{q}\:,\:{r}\:\:\:\:{are}\:\:{roots}\:{of} \\ $$$$\:\:\:\:\:{x}^{\:\mathrm{3}} \:−\mathrm{7}{x}^{\:\mathrm{2}} =\left(\mathrm{4}−{x}\right)\left({x}+\mathrm{2}\right) \\ $$$$\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\mathrm{K}\:=\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{qr}}}\:\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{pr}}}\:\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{pq}}}\:=\:? \\ $$$$ \\ $$ Answered…
Question Number 174124 by BHOOPENDRA last updated on 25/Jul/22 $${C}\mathrm{3}^{{n}} −\mathrm{4}{C}^{\mathrm{3}{n}−\mathrm{1}} =\mathrm{3}^{{n}} \\ $$$${find}\:{C}\:\:{for}\:{any}\:{n}\: \\ $$ Commented by mr W last updated on 25/Jul/22 $${it}'{s}\:{impossible}\:{to}\:{find}\:{a}\:{formula}\:{for}…
Question Number 174092 by behi834171 last updated on 24/Jul/22 $$\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{ax}}^{\mathrm{2}} +\mathrm{14}\boldsymbol{{x}}−\mathrm{210}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{x}}_{\mathrm{1}} .\boldsymbol{{x}}_{\mathrm{2}} =\mathrm{22},\:\:\:\:\:\:\:\boldsymbol{{a}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 24/Jul/22…
Question Number 108553 by I want to learn more last updated on 17/Aug/20 $$\mathrm{If}\:\:\:\:\mathrm{a}_{\mathrm{1}} ,\:\:\mathrm{a}_{\mathrm{2}} ,\:\:\mathrm{a}_{\mathrm{3}} ,\:\:\:\:\mathrm{be}\:\mathrm{an}\:\mathrm{AP},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\mathrm{2m}} {\sum}}\:\left(−\:\mathrm{1}\right)^{\mathrm{n}\:\:−\:\:\mathrm{1}} \:\mathrm{a}_{\mathrm{n}} ^{\mathrm{2}} \:\:\:\:=\:\:\:\frac{\mathrm{m}}{\mathrm{2m}\:\:−\:\:\mathrm{1}}\left(\mathrm{a}_{\mathrm{n}} ^{\mathrm{2}}…
Question Number 174084 by AgniMath last updated on 24/Jul/22 Commented by infinityaction last updated on 24/Jul/22 $$\frac{\sqrt{\mathrm{3}+{x}}+\sqrt{\mathrm{3}−{x}}+\sqrt{\mathrm{3}+{x}}−\sqrt{\mathrm{3}−{x}}}{\:\sqrt{\mathrm{3}+{x}}+\sqrt{\mathrm{3}−{x}}−\sqrt{\mathrm{3}+{x}}+\sqrt{\mathrm{3}−{x}}}\:=\:\frac{\mathrm{2}+\mathrm{1}}{\mathrm{2}−\mathrm{1}} \\ $$$$\:\:\frac{\sqrt{\mathrm{3}+{x}}}{\:\sqrt{\mathrm{3}−{x}}}\:=\:\mathrm{3} \\ $$$$\:\:\frac{\mathrm{3}+{x}}{\mathrm{3}−{x}}\:=\:\mathrm{9} \\ $$$$\:\:\:\frac{\mathrm{6}}{\mathrm{2}{x}}\:=\:\frac{\mathrm{10}}{\mathrm{8}\:}\:\:\Rightarrow\:{x}\:=\:\frac{\mathrm{24}}{\mathrm{10}} \\ $$$$\:\:{x}\:\:\:=\:\:\frac{\mathrm{12}}{\mathrm{5}}…
Question Number 174074 by AgniMath last updated on 24/Jul/22 Commented by infinityaction last updated on 24/Jul/22 $${ay}\:=\:{bx}\:,\:{cy}\:={bz}\:,\:{cx}\:=\:{az} \\ $$$$\frac{{ax}−{by}}{\left({a}+{b}\right)\left({x}−{y}\right)}+\frac{{by}−{cz}}{\left({b}+{c}\right)\left({y}−{z}\right)}+\frac{{cz}−{ax}}{\left({c}+{a}\right)\left({z}−{x}\right)}\: \\ $$$$\frac{{ax}−{by}}{\left({a}+{b}\right)\left({x}−{y}\right)}−\mathrm{1}+\frac{{by}−{cz}}{\left({b}+{c}\right)\left({y}−{z}\right)}−\mathrm{1}+\frac{{cz}−{ax}}{\left({c}+{a}\right)\left({z}−{x}\right)}−\mathrm{1}+\mathrm{3} \\ $$$$\frac{{ay}−{bx}}{\left({a}+{b}\right)\left({x}−{y}\right)}+\frac{{bz}−{cy}}{\left({b}+{c}\right)\left({y}−{z}\right)}+\frac{{cx}−{az}}{\left({c}+{a}\right)\left({z}−{x}\right)}+\mathrm{3} \\ $$$$\:\mathrm{0}+\mathrm{0}+\mathrm{0}+\mathrm{3}\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:…
Question Number 174062 by Tawa11 last updated on 23/Jul/22 $$\mathrm{find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\:\mathrm{such}\:\mathrm{that}\:\:\:\:\mathrm{p}^{\mathrm{2}} \:\:−\:\:\mathrm{p}\:\:\:\:=\:\:\:\mathrm{37q}^{\mathrm{2}} \:\:−\:\:\mathrm{q} \\ $$ Commented by Rasheed.Sindhi last updated on 24/Jul/22 $$\ll_{\bullet} ^{\bullet} \:\underset{−} {\overline…
Question Number 174057 by AgniMath last updated on 23/Jul/22 Commented by dragan91 last updated on 23/Jul/22 $$\mathrm{x}^{\mathrm{7}} −\mathrm{x}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}= \\ $$$$\mathrm{x}\left(\mathrm{x}^{\mathrm{6}} −\mathrm{1}\right)+\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)= \\ $$$$\mathrm{x}\left(\mathrm{x}^{\mathrm{3}}…
Question Number 174059 by mr W last updated on 23/Jul/22 $${if}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\mathrm{3}{xy}=\mathrm{1},\:{then}\:{x}+{y}=? \\ $$ Commented by infinityaction last updated on 23/Jul/22 $${y}\:=\mathrm{0}\:{and}\:{x}\:=\:\mathrm{1} \\ $$$${then}\:{x}+{y}\:=\:\mathrm{1}…