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Category: Algebra

x-1-x-2-x-3-2-x-2-x-4-x-5-x-2-x-2-x-3-x-4-2-x-3-x-5-x-1-x-3-x-3-x-4-x-5-2-x-4-x-1-x-2-x-4-x-4-x-5-x-1-2-x-5-x-2-x-3-x-

Question Number 206074 by MATHEMATICSAM last updated on 06/Apr/24 $$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{2}} \left({x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \:−\:{x}_{\mathrm{2}} \right) \\ $$$$\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{3}} \left({x}_{\mathrm{5}}…

Find-3-4-8-9-15-16-120-121-

Question Number 206066 by hardmath last updated on 06/Apr/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{8}}{\mathrm{9}}\:\centerdot\:\frac{\mathrm{15}}{\mathrm{16}}\:\centerdot\:…\:\centerdot\:\frac{\mathrm{120}}{\mathrm{121}}\:=\:? \\ $$ Answered by mr W last updated on 06/Apr/24 $$\underset{{n}=\mathrm{2}} {\overset{\mathrm{11}} {\prod}}\frac{{n}^{\mathrm{2}}…

If-cos-sin-1-3-Find-sin2-

Question Number 206082 by hardmath last updated on 06/Apr/24 $$\mathrm{If}\:\:\:\mathrm{cos}\boldsymbol{\alpha}\:=\:\mathrm{sin}\boldsymbol{\alpha}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{sin2}\boldsymbol{\alpha}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 29/Apr/24 $$\mathrm{cos}\alpha\:=\:\mathrm{sin}\alpha\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\Rightarrow\:\mathrm{cos}\alpha\:−\:\mathrm{sin}\alpha\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\…

2-2024-x-mod-10-

Question Number 206025 by cortano12 last updated on 05/Apr/24 $$\:\:\:\:\:\mathrm{2}^{\mathrm{2024}} \:=\:{x}\:\left({mod}\:\mathrm{10}\right)\: \\ $$ Answered by BaliramKumar last updated on 05/Apr/24 $$\mathrm{Find}\:\mathrm{unit}\:\mathrm{digit} \\ $$$$\mathrm{2}^{\mathrm{2024}} \:=\:\mathrm{2}^{\mathrm{4k}\:+\:\mathrm{4}} \:=\:\mathrm{2}^{\mathrm{4}}…

If-x-3-2-then-1-x-1-x-1-x-1-x-

Question Number 205990 by MATHEMATICSAM last updated on 04/Apr/24 $$\mathrm{If}\:{x}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{then}\:\frac{\sqrt{\mathrm{1}\:+\:{x}}\:+\:\sqrt{\mathrm{1}\:−\:{x}}}{\:\sqrt{\mathrm{1}\:+\:{x}}\:−\:\sqrt{\mathrm{1}\:−\:{x}}}\:=\:? \\ $$ Answered by cortano12 last updated on 04/Apr/24 $$\:\frac{\left(\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}\:\right)^{\mathrm{2}} }{\mathrm{2}{x}}\:=\:\frac{\mathrm{2}+\mathrm{2}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}{x}}\: \\ $$$$\:=\:\frac{\mathrm{1}}{{x}}\:+\:\sqrt{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\mathrm{1}}\:…

2-2-2-2-2-2-2-2-2-2-3-

Question Number 205941 by cortano12 last updated on 03/Apr/24 $$\:\:\:\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}}\:=?\: \\ $$$$\: \\ $$ Answered by mr W last updated on 03/Apr/24 $$\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}} \\ $$$$=\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{3}}{\mathrm{4}}}}}…

9-Mathematical-Analysis-I-X-d-is-a-metric-space-and-p-n-n-1-is-a-sequence-in-X-such-that-p-n-convergent-p-If-K-p-n-n-1-p-

Question Number 205971 by mnjuly1970 last updated on 03/Apr/24 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{9}\:\:\mathscr{M}{athematical}\:\:\:\:\mathscr{A}{nalysis}\:\left(\:{I}\:\right) \\ $$$$\:\:\left({X}\:,\:{d}\:\right)\:{is}\:{a}\:{metric}\:{space}\:{and}\:\:\:\:\:\:\: \\ $$$$\:\:\:\left\{\:{p}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty} {is}\:{a}\:{sequence}\:{in}\:{X}\: \\ $$$$\:\:\:\:\:{such}\:{that}\:,\:{p}_{{n}} \overset{{convergent}} {\rightarrow}\:{p}\:.\:{If}\:,\:{K}=\:\left\{{p}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty}…