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kostyasuper
@kostyasuper
July 2022
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Решите примеры!! Всё на скринах!
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Tanya11062000
3) система
√x+
√y = 3
2√x+3
√y=7
////////////
√x=3-
√y
3√y + 2*(3-
√y)=7
///////////
√x=3-
√y
3√y+6 -2
√y=7
///////////
√y=1
√x=3-
√y=3-1=2
///////////
y=1
x=4
1 votes
Thanks 0
Utem
3√x+3√y=9 3(√x+√y)=9 √x+√y=3 √x=3-√y
2√x+3√y=7 2√x+3√y=7 2√x+3√y=7 2(3-√y)+3√y=7
6-2√y+3√y=7
6+√y=7
√y=7-6
√y=1
y=1 √x=3-1 √x=2 x=4
Ответ: х=4, у=1
log₀₂(7-x)>-1
(3-x)/(x+2)≥0
ОДЗ:
7-х>0 -x>-7 x<7 ⇒ x∈(-∞;2)∪(2;7)
x+2≠0 x≠-2
7-x<0,2⁻¹ 7-x<5 -x<5-7 x>2
3-x≥0 -x≥-3 x≤3 x≤3
x+2>0 x>-2 x>-2 x>-2
3-x≤0 -x≤-3 x≥3 x≥3
x+2<0 x<-2 x<-2 x<-2
Ответ: x∈(2;3]
logₓ64=3
x³=64
x=∛64
x=4
y²=4
y=2 (y=-2 не подходит т. к. основание логарифма >0)
Ответ: х=4, у=2.
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Thanks 0
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Answers & Comments
√x+√y = 3
2√x+3√y=7
////////////
√x=3-√y
3√y + 2*(3-√y)=7
///////////
√x=3-√y
3√y+6 -2√y=7
///////////
√y=1
√x=3-√y=3-1=2
///////////
y=1
x=4
2√x+3√y=7 2√x+3√y=7 2√x+3√y=7 2(3-√y)+3√y=7
6-2√y+3√y=7
6+√y=7
√y=7-6
√y=1
y=1 √x=3-1 √x=2 x=4
Ответ: х=4, у=1
log₀₂(7-x)>-1
(3-x)/(x+2)≥0
ОДЗ:
7-х>0 -x>-7 x<7 ⇒ x∈(-∞;2)∪(2;7)
x+2≠0 x≠-2
7-x<0,2⁻¹ 7-x<5 -x<5-7 x>2
3-x≥0 -x≥-3 x≤3 x≤3
x+2>0 x>-2 x>-2 x>-2
3-x≤0 -x≤-3 x≥3 x≥3
x+2<0 x<-2 x<-2 x<-2
Ответ: x∈(2;3]
logₓ64=3
x³=64
x=∛64
x=4
y²=4
y=2 (y=-2 не подходит т. к. основание логарифма >0)
Ответ: х=4, у=2.