Question Number 7251 by Tawakalitu. last updated on 19/Aug/16 $${Find}\:{the}\:{value}\:{of}\:{x}\: \\ $$$$ \\ $$$$\left(\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{3}}}\right)^{{x}} \:\:+\:\:\left(\sqrt{\mathrm{2}\:−\:\sqrt{\mathrm{3}}}\right)^{{x}} \:\:=\:\:\mathrm{4} \\ $$ Commented by sou1618 last updated on 19/Aug/16…
Question Number 7234 by WagST last updated on 17/Aug/16 $${need}\:{help}\:{with}\:{step}\:{by}\:{step}.\:{thanks}. \\ $$$$ \\ $$$${x}\left({x}+\mathrm{4}\right)\left({x}−\mathrm{1}\right)=\mathrm{2}{x}\left({x}+\mathrm{4}\right) \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzia last updated…
Question Number 7222 by Tawakalitu. last updated on 16/Aug/16 $${What}\:{are}\:{the}\:{possible}\:{solution}\:{satisfying} \\ $$$${x}^{{y}} \:=\:{y}^{{x}} \\ $$ Commented by Tawakalitu. last updated on 17/Aug/16 $${I}\:{appreciate}\:{your}\:{effort}.\:{thanks}\:{sir}. \\ $$…
Question Number 7207 by Tawakalitu. last updated on 16/Aug/16 $${x}^{\left(\mathrm{2}{x}/{y}\right)} \:\:×\:\:\:{y}^{\left({y}/{x}\right)} \:\:=\:\:\mathrm{4}\:\:\:\:\:\:………….\:\left({i}\right) \\ $$$${xy}^{\left({xy}\:+\:{yx}\right)} \:\:=\:\:\mathrm{16}\:\:\:\:\:…………\:\left({ii}\right) \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$ Commented by Yozzia last…
Question Number 7193 by peter james last updated on 15/Aug/16 Commented by Yozzia last updated on 15/Aug/16 $${S}\left({n}\right)=\mathrm{1}+\mathrm{2}^{\mathrm{2}} −\mathrm{3}^{\mathrm{3}} +\mathrm{4}+\mathrm{5}^{\mathrm{2}} −\mathrm{6}^{\mathrm{3}} +\mathrm{7}+\mathrm{8}^{\mathrm{2}} −\mathrm{9}^{\mathrm{3}} +… \\…
Question Number 7178 by aftab ahmad last updated on 14/Aug/16 Commented by aftab ahmad last updated on 14/Aug/16 $$\boldsymbol{{Very}}\:\boldsymbol{{nice}}\:\boldsymbol{{approach}}\:\boldsymbol{{sir}}..\boldsymbol{{T}}{h}\boldsymbol{{anks}}\:\boldsymbol{{a}}\:\boldsymbol{{lot}}. \\ $$ Commented by Yozzia last…
Question Number 7168 by Tawakalitu. last updated on 14/Aug/16 $${I}\:{have}\:{five}\:{envelopes}\:{numbered}\:\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7}\:{all}\:{hidden}\:{in}\:{a} \\ $$$${box},\:{i}\:{picked}\:{an}\:{envelope}\:.\:\:{If}\:{its}\:{prime}\:{then}\:{i}\:{get}\:{the}\: \\ $$$${square}\:{of}\:{that}\:{number}\:{in}\:{Naira}.\:{Otherwise}\:\left({without}\:\right. \\ $$$$\left.{replacement}\right)\:{i}\:{picked}\:{another}\:{envelope}\:{and}\:{then}\:{get}\:{the} \\ $$$${sum}\:{of}\:{the}\:{squares}\:{of}\:{the}\:{two}\:{numbers}\:{picked}\:\left({in}\:{Naira}\right) \\ $$$${what}\:{is}\:{the}\:{chance}\:{of}\:{me}\:{getting}\:\:{N}\mathrm{25}\:\:? \\ $$$$ \\ $$ Commented…
Question Number 7165 by Tawakalitu. last updated on 15/Aug/16 $$\mathrm{30}\:{teams}\:{participated}\:{in}\:{the}\:{football}\:{tournament}\:.\:{At}\:{the}\: \\ $$$${end}\:{of}\:{the}\:{competition}\:{it}\:{turned}\:{out}\:{that}\:{in} \\ $$$${Any}\:{group}\:{of}\:{three}\:\:{teams}\:{it}\:{is}\:{possible}\:{to}\:{single}\:{out}\:{two} \\ $$$${teams}\:{which}\:{score}\:{equal}\:{point}\:{in}\:{three}\:{games}.\: \\ $$$${within}\:{this}\:{group}\:\left(\mathrm{3}\:{points}\:{are}\:{given}\:{for}\:{the}\:{victory},\:\right. \\ $$$$\left.\mathrm{1}\:{point}\:{for}\:{the}\:{draw}\:,\:\mathrm{0}\:{point}\:{for}\:{the}\:{defeat}\:\right).\: \\ $$$${what}\:{is}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{draws}\:{that}\:{can}\:{occur} \\ $$$${in}\:{such}\:{a}\:{tournament}\:? \\…
Question Number 7161 by Tawakalitu. last updated on 14/Aug/16 $${If}\:\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0},\:\:{prove}\:{that}. \\ $$$${x}\:=\:\frac{\mathrm{2}{c}}{−\:{b}\:\pm\:\sqrt{{b}^{\mathrm{2}} \:−\:\mathrm{4}{ac}}}\: \\ $$ Commented by sou1618 last updated on 14/Aug/16 $$\left(\ast\right)\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}…
Question Number 138235 by mr W last updated on 11/Apr/21 $${for}\:{p},{q}\in\mathbb{R}\:{satisfying}\:{p}^{\mathrm{4}} +{q}^{\mathrm{4}} =\mathrm{4}{pq} \\ $$$${find}\:{the}\:{range}\:{of}\:{p}+{q}\:{when} \\ $$$$\left.\mathrm{1}\right)\:{no}\:{restriction} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{0}\leqslant{p}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{q}\leqslant\mathrm{1} \\ $$ Answered by mr W…