Question

Решить! 1) (х²+6х)²+2(х+3)²=81 2) (х²-2х)²+(х-1)²=1 3) х(х²+6х+9)=4(х+3)

Answer 1

Исходные не пишу.

$x^4 + 12x^3 + 38x^2 + 12x + 18 = 81 x^4 + 12x^3 + 38x^2 + 12x - 63 = 0 (x - 1)(x + 3)^2(x + 7) = 0 x1 = 1 ; x2 = -3 ; x3 = -7$

$x^4 - 4x^3 + 5x^2 - 2x + 1 = 1 x^4 - 4x^3 + 5x^2 - 2x = 0 x(x - 2)(x - 1)^2 = 0 x1 = 2 ; x2 = 1 ; x3 = 0$

$x^3 + 6x^2 + 9x = 4(x+3) x^3 + 6x^2 + 9x = 4x + 12 x^3 + 6x^2 + 5x - 12= 0 (x - 1)(x + 3)(x + 4) = 0 x1 = 1 ; x2 = - 3 ; x3 = - 4$

Answer 2

1)  (x+3)^2=y
(y-9)^2+2(y-9)=81-18
(y-9)^2+2(y-9)+1=64
y1-9=7
y2-9=-9
y1=16
y2=0
x1+3=4  x1=1
x2=-7
x3=-3
ответ: 3 решения х1=1, х2=-7, х3=-3
2)  (х-1)*(х-1)=у
(у-1)^2+(y-1)+1=1
(у-1)^2+(y-1)+0,25=0,25
y1=1
y2=0
x1=0, x2=2,x3=1
3) x (x+3)^2=4(x+3)   x1=-3
x(x+3)=4
x^2+3x+2,25=6,25
(x+1,5)^2=2,5*2,5
x2=1,  x3=-4
ответ : 3 решения  х1=-3,х2=1, х3=-4