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Skyflay12367
Skyflay12367
08.02.2023 11:48 •  Математика

Кнаименьшему общему знаменателю дроби обыкновенные дроби 43/4 и 5/6 и 7/8 9/10 и 1/4 2/15 и 1/6 11/12 и 3/8 1/16 и 5/12 13/18 и 1/10 5/24 и 15/16

👇
Ответ:
belayazima
belayazima
08.02.2023
1)3/4= 9/12  и 1/6 = 2/12
4=2*2 ; 6=2*3 ⇒ НОК ( 4;6) = 2*2*3=12 ⇒НОЗ =12
2) 5/6 = 20/24 и 7/8= 21/24
6= 2*3; 8= 2*2*2 ⇒НОК (3;8) = 2*2*2*3 =24⇒НОЗ=24
3) 9/10= 18/20 и  1/4= 5/20
10=2*5; 4=2*2⇒НОК (10,4)= 2*2*5=20⇒НОЗ=20
4)2/15=4/30 и 1/6=5/30
15=3*5; 6=2*3 ⇒НОК (15,6)= 3*2*5=30 ⇒НОЗ=30
5)11/12= 22/24  и 3/8=9/24
12=2*2*3; 8=2*2*2⇒НОК (12,8)= 2*2*2*3=24⇒НОЗ=24
6) 1/16=3/48 и 5/12=20/48
16=2*2*2*2; 12=2*2*3⇒НОК (16,12)= 2*2*2*2*3=16*3=48; НОЗ=48
7) 13/18= 65/90 и 1/10=9/90
18=3*3*2  10=5*2 ⇒НОК (18;10) =3*3*2*5=90⇒НОЗ=90
8)5/24=10/48 и 15/16=45/48
24= 2*2*2*3; 16=2*2*2*2⇒НОК (24,16)=2*2*2*2*3=16*3=48⇒НОЗ=48
4,4(6 оценок)
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Ответ:
tseng7788
tseng7788
08.02.2023

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4,6(44 оценок)
Ответ:
Бека672
Бека672
08.02.2023
Запишем условие задачи в виде системы уравнений:
{a₁q⁴ - a₁ = 15
{a₁q³ - a₁q = 3.
Вынесем за скобки общий множитель:
{a₁(q⁴ - 1) = 15          {a₁(q² - 1)(q² + 1) = 15     
{a₁q(q² - 1) = 3          {a₁q(q² - 1) = 3.
Разделим левые и правые части равенств первое на второе:
(q² + 1) / q = 5.
Получаем квадратное уравнение:
q² - 5q + 1 = 0.
Квадратное уравнение, решаем относительно q: 
Ищем дискриминант:D=(-5)^2-4*1*1=25-4=21;
Дискриминант больше 0, уравнение имеет 2 корня:
q₁=(√21-(-5))/(2*1)=(√21+5)/2=√21/2+5/2=√21/2+2.5 ≈ 4.791288;
q₂=(-√21-(-5))/(2*1)=(-√21+5)/2=-√21/2+5/2=-√21/2+2.5 ≈ 0.208712.
a₁(₁) = 15 / (q₁⁴ - 1) =  0.028517.
a₁(₂) = 15 / ( (q₂⁴ - 1) =  -15.028517.
Получаем 2 прогрессии:
a_n=0.028517*4.791288^{n-1}.
a_n=-15.028517*0.208712^{n-1}.
4,4(58 оценок)
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