Question

Решите уравнение: 1)6(х+1)^2+2(x-1)(x^2+x+1)-2(x+1)^3=26 2)5x(x-3)^2-5(x-1)^3+15(x+2)(x-2)=5 3)(x+2)^3-x(3x+1)^2+(2x+1)(4x^2-2x+1)=42

Answer 1

$1)6(x+1)^2+2(x-1)(x^2+x+1)-2(x+1)^3=26$

$6x^2+12x+6+2x^3-2-2x^3-6x^2-6x-2-26=0$

$\\ 6x-24=0$

$6x=24$

$\\ x=24:6$

$\\ x=4$

$2)5x(x-3)^2-5(x-1)^3+15(x+2)(x-2)-5=0$

$\\ 5x(x^2-6x+9)-5(x^3-3x^2+3x-1)+15(x^2-4)-5=0$

$\\ 5x^3-30x^2+45x-5x^3+15x^2-15x+5+15x^2-60-5=0$

$\\ 30x-60=0$

$\\ x=2$

$2)(x+2)^3-x(3x+1)^2+(2x+1)(4x^2-2x+1)=42$

$\\ x^3+6x^2+12x+8-9x^3-6x^2-x+8x^3+1-42=0$

$\\ 11x-33=0$

$\\ x=3$