Question

cho a= x²+x+1. Tính A theo a biết A = x⁴ + 2x³ + 5x² + 4x + 4

Answer 1

\(A=\left(x^4+2x^3+x^2\right)+4.\left(x^2+x+1\right)\)

\(A=\left(x^2+x\right)^2+4.a\)

\(A=\left(a-1\right)^2+4a\)

\(A=a^2+2a+1\)

\(A=\left(a+1\right)^2\)

Answer 2

Ta có : \(A=x^4+2x^3+5x^2+4x+4\)

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

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

\(=\left(x^2+x+1\right)\left(x^2+x+3\right)+1\)\(=a\left(a+2\right)+1=a^2+2a+1=\left(a+1\right)^2\)