Question

решите уравнение (х2+х-5) (х2+х+1) =-9

Answer 1

(x²+x-5)(x²+x+1)=-9

x^4+x³+x²+x³+x²+x-5x²-5x-5=-9

x^4+2x³-3x²-4x+4=0

x^4-x³+3x³-3x²-4x+4=0

x³(x-1)+3x²(x-1)-4(x-1)=0

(x-1)(x³+3x²-4)=0

(x-1)(x³-x²+4x²-4)=0

(x-1)(x²(x-1)+4(x²-1))=0

(x-1)(x²(x-1)+4(x+1)(x-1))=0

(x-1)(x-1)(x²+4(x+1))=0

(x-1)(x-1)(x²+4x+4)=0

(x-1)²(x+2)²=0

x1=1

x2=-2