Question

cho 2 da thuc:f(x)=x^2+3mx+m^2 va g(x)=x^2+(2m-1)x+m^2. tim m de f(1)=g(1)

Answer 1

Lời giải:

\(f(x)=x^2+3mx+m^2\Rightarrow f(1)=1+3m+m^2\)

\(g(x)=x^2+(2m-1)x+m^2\Rightarrow g(1)=1+(2m-1)+m^2=m^2+2m\)

Để \(f(1)=g(1)\Leftrightarrow 1+3m+m^2=m^2+2m\)

\(\Leftrightarrow 1+m=0\Leftrightarrow m=-1\)

Vậy \(m=-1\)

Answer 2

\(\left\{{}\begin{matrix}f\left(x\right)=x^2+3mx+m^2\\g\left(x\right)=x^2+\left(2m-1\right)x+m^2\end{matrix}\right.\)

\(h\left(x\right)=f\left(x\right)-g\left(x\right)=\left[3m-\left(2m-1\right)\right]x=\left(m+1\right)x\)

\(f\left(1\right)=g\left(1\right)\Rightarrow f\left(1\right)-g\left(1\right)=0\Rightarrow h\left(1\right)=0\)

\(\Rightarrow\left(m+1\right).1=0\Rightarrow m=-1\)