Question

Решить уравнение $(x^2-7x+8)(x^2+9x+8)=-39x^2$

Answer 1

Ответ:

(x

2

−7x+8)∗(x

2

+9x+8)=−39x

2

x^4+9x^3+8x^2-7x^3-63x^2-56x+8x^2+72x+64=-39x^2x

4

+9x

3

+8x

2

−7x

3

−63x

2

−56x+8x

2

+72x+64=−39x

2

x^4+2x^3-47x^2+16x+64=-39x^2x

4

+2x

3

−47x

2

+16x+64=−39x

2

x^4+2x^3-47x^2+16x+64+39x^2=0x

4

+2x

3

−47x

2

+16x+64+39x

2

=0

x^4+2x^3-8x^2-16x+32x+64=0x

4

+2x

3

−8x

2

−16x+32x+64=0

x^3*(x+2)-8x*(x+2)+32(x+2)=0x

3

∗(x+2)−8x∗(x+2)+32(x+2)=0

(x+2)*(x^3-8x+32)=0(x+2)∗(x

3

−8x+32)=0

(x+2)*(x^3-16x+8x+32)=0(x+2)∗(x

3

−16x+8x+32)=0

(x+2)*(x*(x^2-16)+8(x+4))=0(x+2)∗(x∗(x

2

−16)+8(x+4))=0

(x+2)*(x*(x-4)*(x+4)+8(x+4))=0(x+2)∗(x∗(x−4)∗(x+4)+8(x+4))=0

(x+2)*(x+4)*(x*(x-4)+8)=0(x+2)∗(x+4)∗(x∗(x−4)+8)=0

(x+2)*(x+4)*(x^2-4x+8)=0(x+2)∗(x+4)∗(x

2

−4x+8)=0

x+2=0x+2=0

x+4=0x+4=0

x^2-4x+8=0x

2

−4x+8=0

x₁= -4, x₂ = -2