1) x³-49x=0

2) 7x² = (2x+1) ²+3x²-5

3) (x-2) ³ + (x+2) ³=2x (x²-1) + 3

4) x³-3x²+2x-6=0

5) x³+2x²-9x-18=0

6) 7 - (2x-2) * (4x+1) = 2x * (5-4x)

7) (5-x) ² - (3x-2) * (2x+1) = x * (2-5x)

1) x³-49x=0

x (x²-49) = 0

x (x-7) (x+7) = 0

x₁=0

x-7=0

x₂=7

x+7=0

x₃=-7

2) 7x² = (2x+1) ²+3x²-5

7x²=4x²+4x+1+3x²-5

7x²=7x²+4x-4

7x²+4x-4-7x²=0

4x-4=0

4x=4

x=4:4

x=1

3) (x-2) ³ + (x+2) ³=2x (x²-1) + 3

(x-2+x+2) ((x-2) ² - (x-2) (x+2) + (x+2) ²) = 2x³-2x+3

2x (x²-4x+4-x²+4+x²+4x+4) = 2x³-2x+3

2x (x²+12) = 2x³-2x+3

2x³+24x=2x³-2x+3

2x³+24x-2x³+2x=3

26x=3

x=26/3

4) x³-3x²+2x-6=0

x² (x-3) + 2 (x-3) = 0

(x²+2) (x-3) = 0

x=3

5) x³+2x²-9x-18=0

x² (x+2) - 9 (x+2) = 0

(x²-9) (x+2) = 0

(x-3) (x+3) (x+2) = 0

x-3=0

x=3

x+3=0

x=-3

x+2=0

x=-2

6) 7 - (2x-2) * (4x+1) = 2x * (5-4x)

7 - (6x²-8x+2x-2) = 10x-8x²

7 - (6x²-6x-2) = 10x-8x²

7-6x²+6x+2=10x-8x²

-6x²+6x+9+8x²-10x=0

2x²-4x+9=0

D=4*4-4*2*9=16-72=-56<0 корней нет

7) (5-x) ² - (3x-2) * (2x+1) = x * (2-5x)

(25-10 х+х²) - (6 х²-4x+3x-2) = 2x-5x²

25-10x+x²-6x²+x+2=2x-5x²

-5x²-9x+27=2x-5x²

2x+9x=27

11x=27

x=27/11