Помогите решить пример только полностью и с описанием. Created by sum2002. matematika-ru

Перепишем нашу систему в виде:сделаем замену:х-у=ах+у=bв первом уравнении введем заменуполучим значит, делая обратную замену t=a/b, получаем, что наша система эквивалентна двум следующим: первая система{a/b=3{a•b=12a=3b3b²=12 b¹'²=±2a¹'²=±6вторая система {a/b=¼{a•b=12b=4a4a²=12a³'⁴=±√3b³'⁴=±4√3получили 4 значения а и bвозвращаемся к заменех-у=ах+у=bполучаем 4 системы с переменными х и уи находим их (1)а¹=6, b¹=2{х-у=6{х+у=22x=8x¹=4y¹= - 2(2)а²=-6, b²=-2{х-у= - 6{х+у= - 2x²= -4у²=2(3)а³=√3b³=4√3{х-у= √3{х+у= 4√32x³=5√3x³=2,5√3y³=1,5√3(4)а³= - √3b³= - 4√3{х-у= -√3{х+у=- 4√3x⁴= -2,5√3y⁴= -1,5√3Ответ :x¹=4y¹= - 2x²= -4у²=2x³=2,5√3y³=1,5√3x⁴= -2,5√3y⁴= -1,5√3Новые вопросы в МатематикаІз заліза виплавили три прямокутні паралелепіпеди з ребрами 3, 4 і 5 дм. Потім їх усі розплавили і виплавили один куб. Який його об’єм (у дм3 )? Помог…ите пж...Кімната має розміри 3 м на 4 м, а висота кімнати дорівнює 3 м. Скільки фарби потрібно для того, щоб пофарбувати стелю та стіни цієї кімнати, якщо витр…ати фарби становлять 300 г на 1 м2? СРОЧНО!!!пж помогите умоляю пж помогите п умоляю пж помогите пж умоляю Пожалуйста очень срочно!!3. Власна швидкість човна 9 км/год, а швидкість течії річки 3 км/год. Відстаньміж пристанями 24 км. Скільки часу витратить…човен на шлях між присталями«туди» і «назад»?3. Власна швидкість човна 9 км/год, а швидкість течії річки 3 км/год. Відстаньміж пристанями 24 км. Скільки часу витратить човен на шлях між присталя…ми«туди» і «назад»?3. По річці, швидкість течії якоï 1 км/год, плив за течією моторний човен звласною швидкістю 8 км/год. Байдарка пливла по тій самій річці проти течії…звласною швидкістю 4 км/год. Байдарка витратила на весь шлях утричі більшечасу, ніж моторний човен. Яке судно пройшло більшу відстань?А. Моторний човенБ. Байдарка.В. Визначити не можливо.Г. Відстані однаковіСплав вагою 5 кг містить 28% срібла. 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Помогите решить пример только полностью и с описанием...

sum2002 @sum2002

July 2022 1 11 Report

Помогите решить пример только полностью и с описанием

Answers & Comments

spasibo3pajbrh Перепишем нашу систему в виде:
$\frac{4(x - y)}{x + y} + \frac{3(x + y)}{x - y} = 13 \\( x - y)(x + y) = 12$
сделаем замену:
х-у=а
х+у=b

$\frac{4a}{b} + \frac{3b}{a} = 13 \\ a \: \cdot \: b = 12$

в первом уравнении введем замену

$\frac{a}{b} = t$

получим

$4t + \frac{3}{t} = 13 \\ 4 {t }^{2} - 13t + 3 = 0 \\ t_1,_2= \frac{13± 11}{8} \\ t_1 = 3 \\ t_2 = \frac{1}{4}$
значит, делая обратную замену t=a/b, получаем, что наша система эквивалентна
двум следующим:

первая система
{a/b=3
{a•b=12

a=3b
3b²=12
b¹'²=±2
a¹'²=±6

вторая система
{a/b=¼
{a•b=12

b=4a
4a²=12
a³'⁴=±√3
b³'⁴=±4√3

получили 4 значения а и b
возвращаемся к замене
х-у=а
х+у=b
получаем 4 системы с переменными х и у

и находим их

(1)
а¹=6,
b¹=2

{х-у=6
{х+у=2

2x=8
x¹=4
y¹= - 2

(2)
а²=-6,
b²=-2
{х-у= - 6
{х+у= - 2

x²= -4
у²=2

(3)
а³=√3
b³=4√3

{х-у= √3
{х+у= 4√3
2x³=5√3

x³=2,5√3
y³=1,5√3

(4)
а³= - √3
b³= - 4√3

{х-у= -√3
{х+у=- 4√3

x⁴= -2,5√3
y⁴= -1,5√3

Ответ :

x¹=4
y¹= - 2

x²= -4
у²=2

x³=2,5√3
y³=1,5√3

x⁴= -2,5√3
y⁴= -1,5√3