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al77op
@al77op
July 2022
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(x-3)√(2x-3)=(4-x)(x-3)
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m11m
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(x-3)√(2x-3) - (4-x)(x-3)=0
(x-3)(√(2x-3) - (4-x)) =0
x-3=0 √(2x-3) -(4-x) =0
x=3 √(2x-3)=4-x
ОДЗ: 2x-3≥0 и 4-x≥0
2x≥3 -x≥ -4
x≥1.5 x≤4
x∈[1.5; 4]
2x-3=(4-x)²
2x-3=16-8x+x²
-x²+2x+8x-3-16=0
-x²+10x-19=0
x²-10x+19=0
D=(-10)² -4*19=100-76=24=(2√6)²
x₁=(10-2√6)/2=5-√6
x₂=5+√6 ∉ [1.5; 4] - не подходит
Ответ: 5-√6; 3.
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Answers & Comments
Verified answer
(x-3)√(2x-3) - (4-x)(x-3)=0(x-3)(√(2x-3) - (4-x)) =0
x-3=0 √(2x-3) -(4-x) =0
x=3 √(2x-3)=4-x
ОДЗ: 2x-3≥0 и 4-x≥0
2x≥3 -x≥ -4
x≥1.5 x≤4
x∈[1.5; 4]
2x-3=(4-x)²
2x-3=16-8x+x²
-x²+2x+8x-3-16=0
-x²+10x-19=0
x²-10x+19=0
D=(-10)² -4*19=100-76=24=(2√6)²
x₁=(10-2√6)/2=5-√6
x₂=5+√6 ∉ [1.5; 4] - не подходит
Ответ: 5-√6; 3.