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August 2022
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3 x^{4} * 3 x^{3} -8 x^{2} -2х+4=0
найти действительные корни уравнения
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sangers1959
Verified answer
3x⁴+3x³-⁸x²-2x+4=0
x₁=1
3x⁴+3x³-8x²-2x+4 I_x-1_
3x⁴-3x³ I 3x³+6x²-2x-4
----------
6x³-8x²
6x³-6x²
-----------
-2x²-2x
-2x²+2x
-----------
-4x+4
-4x+4
--------
0
3x³+6x²-2x-4=0
x₂=-2
3x³+6x²-2x-4 I_x+2_
3x³+6x² I 3x²-2
-----------
-2x-4
-2x-4
--------
0
3x²-2=0
3x²=2
x²=2/3
x₃=√(2/3)≈0,8165
x₄=√(2/3)≈-0,8165.
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Answers & Comments
Verified answer
3x⁴+3x³-⁸x²-2x+4=0x₁=1
3x⁴+3x³-8x²-2x+4 I_x-1_
3x⁴-3x³ I 3x³+6x²-2x-4
----------
6x³-8x²
6x³-6x²
-----------
-2x²-2x
-2x²+2x
-----------
-4x+4
-4x+4
--------
0
3x³+6x²-2x-4=0
x₂=-2
3x³+6x²-2x-4 I_x+2_
3x³+6x² I 3x²-2
-----------
-2x-4
-2x-4
--------
0
3x²-2=0
3x²=2
x²=2/3
x₃=√(2/3)≈0,8165
x₄=√(2/3)≈-0,8165.