Question

Cho đa thức ; P(x) = 8x² - m²x - 5m và Q( x) = \(\frac{3m}{2}\) - x³ . Tìm số nguyên m thỏa mãn P(-1) = Q( -2 )

 

Answer 1

Ta có \(P\left(-1\right)=8\left(-1\right)^2-m^2\left(-1\right)-5m=8+m^2-5m\)

\(Q\left(-2\right)=\frac{3m}{2}-\left(-2\right)^3=\frac{3m}{2}+8\)

\(8+m^2-5m=\frac{3m}{2}+8\)

\(\Rightarrow m^2-5m=\frac{3m}{2}\)

\(\Rightarrow m^2=\frac{3m}{2}+5m=\frac{3m}{2}+\frac{10m}{2}=\frac{13m}{2}\)

\(\Rightarrow2m^2=13m\Rightarrow\frac{2m^2}{m}=\frac{13m}{m}\)

\(\Rightarrow2m=13\Rightarrow m=\frac{13}{2}\)