Toán Lớp 8: x^2-x-6 b)X^4=4x^2-5 c)x^2-19x-30 d)x^4=x^2=1

Question

Toán Lớp 8:  x^2-x-6            b)X^4=4x^2-5            c)x^2-19x-30         d)x^4=x^2=1

ngocbichchau · Answer

Giải đáp + giải th&iacute;ch c&aacute;c bước giải:     a) x^2-x-6   =x^2-3x+2x-6   =x(x-3)+2(x-3)   =(x+2)(x-3)   b) x^4+4x^2-5   =x^4-x^3+x^3-x^2+5x^2-5x+5x-5   =x^3(x-1)+x^2(x-1)+5x(x-1)+5(x-1)   =(x^3+x^2+5x+5)(x-1)   =[x^2(x+1)+5(x+1)](x-1)   =(x^2+5)(x+1)(x-1)   c) x^2-19x-30   =x^2-2.x .19/2 +361/4-481/4   =(x-19/2)^2-481/4   =(x-19/2- sqrt{481}/2)(x-19/2+ sqrt{481}/2)   d) x^4+x^2+1   =x^4+x^3+x^2-x^3-x^2-x+x^2+x+1   =x^2(x^2+x+1)-x(x^2+x+1)+x^2+x+1   =(x^2-x+1)(x^2+x+1)

daolanhoa · Answer

Giải đáp:   x^2-x-6   =x^2+2x-3x-6   =x(x+2)-3(x+2)   =(x+2)(x-3)   b)x^4+4x^2-5   =x^4+4x^2+4-9   =(x^2+2)^2-3^2   =(x^2-1)(x^2+5)   =(x-1)(x+1)(x^2+5)   c)x^2-19x-30   =x^2-2*x*19/2+361/4-241/4   =(x-19/2)^2-481/4   =(x-19/2-sqrt{481}/2)(x-19/2+sqrt{481}/2)   d)x^4+x^2+1   =x^4+2x^2+1-x^2   =(x^2+1)^2-x^2   =(x^2-x+1)(x^2+x+1).