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Buonanotte
@Buonanotte
July 2022
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решите пожалуйста x^4=(2x-3)^2
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sangers1959
Verified answer
X⁴=(2x-3)²
x⁴=4x²-12x+9
x⁴-4x²+12x-9=0
x₁=1
x⁴-4x²+12x-9 I_x-1_
x⁴-x³ I x³+x²-3x+9
------
x³-4x²
x³-x²
--------
-3x²+12x
-3x²+3x
------------
9x-9
9x-9
-------
0
x³+x²-3x+9=0
x₂=-3
x³+x²-3x+9 I_x+3_
x³+3x² I x²-2x+3
---------
-2x²-3x
-2x²-6x
----------
3x+9
3x+9
-------
0
x²-2x+3=0 D=-8 ⇒
Уравнение не имеет действительных корней.
Ответ: x₁=1 x₂=-3.
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Answers & Comments
Verified answer
X⁴=(2x-3)²x⁴=4x²-12x+9
x⁴-4x²+12x-9=0
x₁=1
x⁴-4x²+12x-9 I_x-1_
x⁴-x³ I x³+x²-3x+9
------
x³-4x²
x³-x²
--------
-3x²+12x
-3x²+3x
------------
9x-9
9x-9
-------
0
x³+x²-3x+9=0
x₂=-3
x³+x²-3x+9 I_x+3_
x³+3x² I x²-2x+3
---------
-2x²-3x
-2x²-6x
----------
3x+9
3x+9
-------
0
x²-2x+3=0 D=-8 ⇒
Уравнение не имеет действительных корней.
Ответ: x₁=1 x₂=-3.