Разложение на множители. 1) Решить в целых числах уравнение x^3

July 2022 1 1 Report

Разложение на множители. 1) Решить в целых числах уравнение x^3 - y^3 = 2044 Выделение целой части. 2) Найти натуральные решения уравнения x·y - 11·(x + y) = 1

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nafanya2014

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1) x³-y³=(x-y)(x²+xy+y²)

(x-y)(x²+xy+y²)=2044

(x-y)(x²+xy+y²)=2²·7·73

$\left \{ {{x-y=1} \atop {x^2+xy+y^2=2044}} \right.$

$\left \{ {{x-y=2} \atop {x^2+xy+y^2=1022}} \right. \left \{ {{x-y=4} \atop {x^2+xy+y^2=511}} \right. \left \{ {{x-y=7} \atop {x^2+xy+y^2=292}} \right. \left \{ {{x-y=14} \atop {x^2+xy+y^2=146}} \right. \left \{ {{x-y=28} \atop {x^2+xy+y^2=73}} \right.$

$\left \{ {{x-y=73} \atop {x^2+xy+y^2=28}} \right. \left \{ {{x-y=146} \atop {x^2+xy+y^2=14}} \right. \left \{ {{x-y=292} \atop {x^2+xy+y^2=7}} \right. \left \{ {{x-y=511} \atop {x^2+xy+y^2=4}} \right.\left \{ {{x-y=1022} \atop {x^2+xy+y^2=2}} \right.$

$\left \{ {{x-y=2044} \atop {x^2+xy+y^2=1}} \right.$

$\left \{ {{x-y=-1} \atop {x^2+xy+y^2=-2044}} \right.$

$\left \{ {{x-y=-2} \atop {x^2+xy+y^2=-1022}} \right. \left \{ {{x-y=-4} \atop {x^2+xy+y^2=-511}} \right. \left \{ {{x-y=-7} \atop {x^2+xy+y^2=-292}} \right. \left \{ {{x-y=-14} \atop {x^2+xy+y^2=-146}} \right. \left \{ {{x-y=-28} \atop {x^2+xy+y^2=-73}} \right.$

$\left \{ {{x-y=-73} \atop {x^2+xy+y^2=-28}} \right. \left \{ {{x-y=-146} \atop {x^2+xy+y^2=-14}} \right. \left \{ {{x-y=-292} \atop {x^2+xy+y^2=-7}} \right. \left \{ {{x-y=-511} \atop {x^2+xy+y^2=-4}} \right.\left \{ {{x-y=-1022} \atop {x^2+xy+y^2=-2}} \right.$

$\left \{ {{x-y=-2044} \atop {x^2+xy+y^2=-1}} \right.$

Решим эти 24 системы способом подстановки и получим решение системы:

{x-y=4

{x^2+xy+y^2=511

ответ (15;11)

2) xy-11x-11y=1⇒ x(y-11)=1+11y

$x=\frac{11y+1}{y-11}=11+\frac{122}{y-11}$

y-11 делится на 122 нацело

при y=12;тогда х=133;

при y=13;тогда х=72;

при y=72; тогда x=13

при y=133; тогда х=12

2 votes Thanks 1

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reshit v celyh chislah19x2 98y2 1998

1 dokazhite chto pri lyubom naturalnom n chislo 21n 4n2 delitsya na 17 2na

dokazat chto 21n 4n2 delitsya na 17

metodom mat indukcii dokazat chto 21n 4n2 delitsya na 17

najti dva naturalnyh chisla ne prevyshayushih 200 raznost mezhdu kotorymi ravna 1

metodom spuska reshit v celyh chislahx2 6y2 5z2

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