Question

Tìm P biết: \(a^2P+2aP+a^2=4\)

Answer 1

\(a^2P+2aP+a^2=4\)

\(\Leftrightarrow\)\(\left(a^2P+2aP\right)+\left(a^2-4\right)=0\)

\(\Leftrightarrow\)\(aP\left(a+2\right)+\left(a-2\right)\left(a+2\right)=0\)

\(\Leftrightarrow\)\(\left(a+2\right)\left(aP+a-2\right)=0\)

\(\Leftrightarrow\)\(\left[{}\begin{matrix}a+2=0\\aP+a-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}a=-2\\P=\dfrac{2}{a}-1\end{matrix}\right.\)

Vậy \(P=\dfrac{2}{a}-1\)

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