Question

Punctul c)
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Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle\int_0^a\dfrac{2x+1}{f(x)}dx=\int_0^a\dfrac{2x+1}{x^2+x+1}dx=\ln(x^2+x+1)|_0^a=\ln(a^2+a+1)\\\texttt{Obtinem }\ln(a^2+a+1)=\ln 3\\a^2+a+1=3\\a^2+a-2=0\\\Delta=1+8=9\Rightarrow \sqrt{\Delta}=3\\a_1=\dfrac{1+3}{2}=\dfrac{4}{2}=2\\a_2=\dfrac{1-3}{2}=-\dfrac{2}{2}=-1\texttt {(nu e pozitiv )}\\\texttt{Prin urmare }\boxed{a=2}$