Question

Решите уравнение: 3x^4 + 7x^3 − 4x^2 + 7x + 3 = 0.

Answer 1

Ответ:

x1 = - 3

x2 = - 1/3

Объяснение:

3x⁴ + 7x³ - 4x² + 7x + 3 = 0

3x⁴ + x³ + 6x³ + 2x² - 6x² - 2x + 9x + 3 = 0

x³ × ( 3x + 1 ) + 2x² × ( 3x + 1 ) - 2x × ( 3x + 1 ) + 3( 3x + 1 ) = 0

( 3x + 1 ) × ( x³ + 2x² - 2x + 3 ) = 0

( 3x + 1 ) × ( x³ + 3x² - x² - 3x + x + 3 ) = 0

( 3x + 1 ) × ( x² × ( x + 3 ) - x × ( x + 3 ) + 1( x + 3 )) = 0

( 3x + 1 ) × ( x + 3 ) × ( x² - x + 1 ) = 0

3x + 1 = 0

x + 3 = 0

x² - x + 1 = 0

x = - 1/3

x = - 3

x Є R

x1 = - 3

x2 = - 1/3

Answer 2

Объяснение:

3х⁴+7х³-4х²+7х+3=0

3х⁴+х³+6х³-4х²+7х+3=0

3х⁴+х³+6х³+2х²-6х²+7х+3=0

3х⁴+х³+6х³+2х²-6х²-2х+9х+3=0

х³(3х+1)+6х³+2х²-6х²-2х+9х+3=0

х³(3х+1)+2х²(3х+1)-6х²-2х+9х+3=0

х³(3х+1)+2х²(3х+1)-2х(3х+1)+9х+3=0

х³(3х+1)+2х²(3х+1)-2х(3х+1)+3(3х+1)=0

(3х+1)(х³+2х²-2х+3)=0

3х+1=0 х³+2х²-2х+3=0

3х= -1 х³+3х²-х²-2х+3=0

х1= -1/3 х³+3х²-х²-3х+х+3=0

х²(х+3)-х²-3х+х+3=0

х²(х+3)-х(х+3)+х+3=0

х²(х+3)-х(х+3)+(х+3)=0

(х+3)(х²-х+1)=0

х+3=0 х²-х+1=0

х2= -3 D=(-1)²-4×1×1= -3

x3∉R

Ответ: х1= -1/3 ; х2= -3