y=19x^2+6x+5 A(x)=9x^2+6x+5=0 D=36 360 lt;0 ⇒ A(x) is possitive ∀ x∈ R max(y)=1min(9x^2+6x+5) =1 DA=4(9)324=19 ...

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General Solution of a Differential Equation

Solve 19x2 ...

Question

Solve $\frac{1}{9 x^{2} + 6 x + 5}$

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Solution

$y = \frac{1}{9 x^{2} + 6 x + 5}$
$A (x) = 9 x^{2} + 6 x + 5 = 0$
$D = 36 - 360 < 0$
$\Rightarrow A (x)$ is possitive $\forall x \in R$
$m a x (y) = \frac{1}{m i n (9 x^{2} + 6 x + 5)}$
$= \frac{1}{\frac{- D}{A}} = \frac{4 (9)}{324} = \frac{1}{9}$

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