Respostas

  • Usuário do Brainly
2013-05-31T00:14:13-03:00

Temos que:

 

\text{f}(\text{x})=\text{x}^2-3\text{x}+5

 

Depois disso, observe que:

 

\text{f}(\text{a})=\text{a}^2-3\text{a}+5

 

\text{f}(\text{a}+1)=(\text{a}+1)^2-3\cdot(\text{a}+1)+5=\text{a}^2-\text{a}+3

 

\text{f}(2\text{a})=(2\text{a})^2-3\cdot2\text{a}+5=4\text{a}^2-6\text{a}+5

 

Logo, podemos afirmar que:

 

\text{a}^2-3\text{a}+5-(\text{a}^2-\text{a}+3)=\dfrac{1}{3}\cdot(4\text{a}^2-6\text{a}+5)

 

-2\text{a}+2=\dfrac{4\text{a}^2-6\text{a}+5}{3}

 

-6\text{a}+6=4\text{a}^2-6\text{a}+5

 

4\text{a}^2+5=6

 

\text{a}^2=\dfrac{1}{4}

 

\text{a}=\dfrac{1}{2}