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)
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)
Answers & Comments
Verified answer
1) x³-49x=0x(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)
(25-10х+х²)-(6х²-4x+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