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Category: Algebra

solve-x-y-N-3x-5y-20-

Question Number 163770 by mnjuly1970 last updated on 10/Jan/22 $$ \\ $$$$\:\:\:\:\:{solve}\::\:\:\:\:{x},{y}\:\in\:\mathbb{N}\: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{3}{x}\:+\:\mathrm{5}{y}\:=\:\mathrm{20}\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$ Answered by MJS_new last updated…

If-x-1-and-x-2-are-roots-of-the-equation-acos-2x-bsin-x-c-and-2sin-x-1-sinx-2-sin-x-1-sinx-2-Then-the-value-of-b-c-a-is-

Question Number 32682 by rahul 19 last updated on 31/Mar/18 $$\boldsymbol{{I}}{f}\:{x}_{\mathrm{1}} \:{and}\:{x}_{\mathrm{2}\:} \:{are}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${acos}\:\mathrm{2}{x}+{bsin}\:{x}\:=\:{c}\:{and}\: \\ $$$$\mathrm{2}{sin}\:{x}_{\mathrm{1}} {sinx}_{\mathrm{2}} =\:{sin}\:{x}_{\mathrm{1}} +{sinx}_{\mathrm{2}} .\:\boldsymbol{{T}}{hen}\: \\ $$$${the}\:{value}\:{of}\:\:\frac{{b}}{{c}−{a}}\:{is}\:? \\ $$…

Total-no-of-polynomials-of-the-form-x-3-ax-2-bx-c-that-are-divisible-by-x-2-1-where-a-b-c-1-2-3-10-is-1-10-2-15-3-5-4-8-

Question Number 32681 by rahul 19 last updated on 31/Mar/18 $$\boldsymbol{{T}}{otal}\:{no}.\:{of}\:{polynomials}\:{of}\:{the}\:{form} \\ $$$${x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:\:{that}\:{are}\:{divisible}\:{by}\: \\ $$$${x}^{\mathrm{2}} +\mathrm{1},\:{where}\:{a},{b},{c}\in\mathrm{1},\mathrm{2},\mathrm{3},….,\mathrm{10}\:{is}\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{10} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{15} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{5} \\…

Find-the-nth-term-of-the-sequence-a-n-such-that-a-1-a-2-a-n-n-n-1-n-n-1-2-3-

Question Number 98215 by I want to learn more last updated on 12/Jun/20 $$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{nth}}\:\:\boldsymbol{\mathrm{term}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sequence}}\:\:\left\{\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \right\}\:\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{a}}_{\mathrm{1}} \:+\:\:\boldsymbol{\mathrm{a}}_{\mathrm{2}} \:+\:\:…\:\:+\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} }{\boldsymbol{\mathrm{n}}}\:\:\:=\:\:\boldsymbol{\mathrm{n}}\:\:+\:\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}}\:\:\left(\boldsymbol{\mathrm{n}}\:\:=\:\:\mathrm{1},\:\:\mathrm{2},\:\:\mathrm{3},\:\:…\right) \\ $$ Commented by Don08q…

Find-the-nth-term-of-the-sequence-a-n-such-that-a-1-1-a-n-1-1-2-a-n-n-2-2n-1-n-2-n-1-2-n-1-2-3-

Question Number 98205 by I want to learn more last updated on 12/Jun/20 $$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{nth}}\:\:\boldsymbol{\mathrm{term}}\:\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sequence}}\:\:\left\{\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \right\}\:\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{a}}_{\mathrm{1}} \:\:=\:\:\mathrm{1},\:\:\:\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:\:+\:\:\frac{\boldsymbol{\mathrm{n}}^{\mathrm{2}} \:−\:\mathrm{2}\boldsymbol{\mathrm{n}}\:\:−\:\:\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}\right)^{\mathrm{2}} }\:\:\:\:\left(\boldsymbol{\mathrm{n}}\:\:=\:\:\mathrm{1},\:\:\mathrm{2},\:\:\mathrm{3},\:\:…\right) \\ $$…