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Эльзарааа
@Эльзарааа
July 2022
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Решите уравнение √(3-2х)-√(1-х)=1
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sedinalana
Verified answer
ОДЗ
3-2x≥0⇒2x≤3⇒x≤1,5
1-x≥0⇒x≤1
x∈(-∞;1]
Возведем в квадрат
3-2x+1-x-2√[(3-2x)(1-x)]=1
2√[(3-2x)(1-x)]=3-3x
Возведем в квадрат
4(3-3x-2x+2x²)=9-18x+9x²
9-18x+9x²-12+20x-8x²=0
x²+2x-3=0
x1+x2=-2 U x1*x2=-3
x1=-3
x2=1
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Answers & Comments
Verified answer
ОДЗ3-2x≥0⇒2x≤3⇒x≤1,5
1-x≥0⇒x≤1
x∈(-∞;1]
Возведем в квадрат
3-2x+1-x-2√[(3-2x)(1-x)]=1
2√[(3-2x)(1-x)]=3-3x
Возведем в квадрат
4(3-3x-2x+2x²)=9-18x+9x²
9-18x+9x²-12+20x-8x²=0
x²+2x-3=0
x1+x2=-2 U x1*x2=-3
x1=-3
x2=1