Question

Cho C= x( x-1)(x-2)-(x^2 -2)(x+3)-4(x-1) . CMR: giá trị của C không phụ thuộc vào x

Answer 1

Sửa đề: \(x\left(x-1\right)\left(x-2\right)-\left(x^2-2\right)\left(x-3\right)-4\left(x-1\right)\)

\(C=x\left(x^2-3x+2\right)-\left(x^3-3x^2-2x+6\right)-4x+4\\ C=x^3-3x^2+2x-x^3+3x^2+2x-6-4x+4\\ C=-2\)

 

Answer 2

\(C=x\left(x-1\right)\left(x-2\right)-\left(x^2-2\right)\left(x-3\right)-4\left(x-1\right)\)

\(=x\left(x^2-3x+2\right)-\left(x^3-3x^2-2x+6\right)-4\left(x-1\right)\)

\(=x^3-3x^2+2x-x^3+3x^2+2x-6-4x+4\)

\(=-2\)