x^2+3x+2= 2/((x^2+3x+3))

解答

x^{2} + 3 x + 2 = \frac{2}{( x ^{2} + 3 x + 3 )}

x = - \frac{- 5 + 3}{2}, x = - \frac{5 + 3}{2}

十进制

x = - 0.38196 \dots, x = - 2.61803 \dots

求解步骤

x^{2} + 3 x + 2 = \frac{2}{( x ^{2} + 3 x + 3 )}

化简

\frac{2}{( x ^{2} + 3 x + 3 )} : \frac{2}{x ^{2} + 3 x + 3}

x^{2} + 3 x + 2 = \frac{2}{x ^{2} + 3 x + 3}

在两边乘以

x^{2} + 3 x + 3

x^{2} (x^{2} + 3 x + 3) + 3 x (x^{2} + 3 x + 3) + 2 (x^{2} + 3 x + 3) = 2

解

x^{2} (x^{2} + 3 x + 3) + 3 x (x^{2} + 3 x + 3) + 2 (x^{2} + 3 x + 3) = 2 : x = - \frac{- 5 + 3}{2}, x = - \frac{5 + 3}{2}

x = - \frac{- 5 + 3}{2}, x = - \frac{5 + 3}{2}

(\frac{x}{( x - 1 )})^{2} + 4 (\frac{x}{( x - 1 )}) + 2 = 0

\frac{( - \frac{4}{3} ) ^{- 2}}{x} = (\frac{8}{15})^{- 1}

x + \frac{3}{x} - 2 - 1 - \frac{x}{x} = \frac{41}{4}

\frac{3}{4 \cdot x ^{2} - 8 x + 3} = 0

2 (\frac{x ^{2} + 1}{x ^{2}}) + 5 (\frac{x + 1}{x}) + 1 = 0