Question

решить уравнение: а) (х+3)³ + 3*(х + 3) = х*(х + 3); б) 3х + 15 = х*(х + 5) ​

Answer 1

$\displaystyle 1)(x+3)^3+3(x+3)=x(x+3)\\(x+3)((x+3)^2+3)=x(x+3)\\(x+3)(x^2+6x+9+3)=x(x+3)\\(x+3)(x^2+6x+12)=x(x+3)\\(x+3)(x^2+6x+12)-x(x+3)=0\\(x+3)(x^2+6x+12-x)=0\\(x+3)(x^2+5x+12)=0\\x+3=0,x^2+5x+12=0\\x=-3,x \notin R\\x=-3\\\\2)3x+15=x(x+5)\\3x+15=x^2+5x\\3x+15-x^2-5x=0\\-2x+15-x^2=0\\2x-15+x^2=0\\x^2+2x-15=0\\x^2+5x-3x-15=0\\x(x+5)-3(x+5)=0\\(x+5)(x-3)=0\\x+5=0,x-3=0\\x_1=-5,x_2=3$