Question

Cho f(x)=x^3-2ax+a^2

g(x)=x^3+(3a+1)x+a^2

a là hằng số

Tìm a để f(1)=g(3)

Answer 1

\(f\left(x\right)=x^3-2ax+a^2\)

\(\Rightarrow f\left(1\right)=1-2a+a^2\)

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

\(\Rightarrow g\left(3\right)=27+\left(3a+1\right)3+a^2\)

Mà \(f\left(1\right)=g\left(3\right)\)

\(\Rightarrow1-2a+a^2=27+\left(3a+1\right)3+a^2\)

\(\Rightarrow1-2a=27+9a+3\)

\(\Rightarrow1-2a=30+9a\)

\(\Rightarrow-29=11a\)

\(\Rightarrow a=\dfrac{-29}{11}\)

Vậy \(a=\dfrac{-29}{11}\) thì \(f\left(1\right)=g\left(3\right)\)