Issolvi f(x)+2f(1/x)=3x+2

$$f ( x ) + 2 f ( \frac { 1 } { x } ) = 3 x + 2$$

Solvi għal f (complex solution)

$$f=\frac{x\left(3x+2\right)}{x^{2}+2}$$

$$x\neq -\sqrt{2}i\text{ and }x\neq \sqrt{2}i\text{ and }x\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x.

$$fxx+2f\times 1=3xx+x\times 2$$

Immultiplika x u x biex tikseb x^{2}.

$$fx^{2}+2f\times 1=3xx+x\times 2$$

Immultiplika x u x biex tikseb x^{2}.

$$fx^{2}+2f\times 1=3x^{2}+x\times 2$$

Immultiplika 2 u 1 biex tikseb 2.

$$fx^{2}+2f=3x^{2}+x\times 2$$

Ikkombina t-termini kollha li fihom f.

$$\left(x^{2}+2\right)f=3x^{2}+x\times 2$$

L-ekwazzjoni hija f'forma standard.

$$\left(x^{2}+2\right)f=3x^{2}+2x$$

Iddividi ż-żewġ naħat b'x^{2}+2.

$$\frac{\left(x^{2}+2\right)f}{x^{2}+2}=\frac{x\left(3x+2\right)}{x^{2}+2}$$

Meta tiddividi b'x^{2}+2 titneħħa l-multiplikazzjoni b'x^{2}+2.

$$f=\frac{x\left(3x+2\right)}{x^{2}+2}$$

Solvi għal f

$$f=\frac{x\left(3x+2\right)}{x^{2}+2}$$

$$x\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x.

$$fxx+2f\times 1=3xx+x\times 2$$

Immultiplika x u x biex tikseb x^{2}.

$$fx^{2}+2f\times 1=3xx+x\times 2$$

Immultiplika x u x biex tikseb x^{2}.

$$fx^{2}+2f\times 1=3x^{2}+x\times 2$$

Immultiplika 2 u 1 biex tikseb 2.

$$fx^{2}+2f=3x^{2}+x\times 2$$

Ikkombina t-termini kollha li fihom f.

$$\left(x^{2}+2\right)f=3x^{2}+x\times 2$$

L-ekwazzjoni hija f'forma standard.

$$\left(x^{2}+2\right)f=3x^{2}+2x$$

Iddividi ż-żewġ naħat b'x^{2}+2.

$$\frac{\left(x^{2}+2\right)f}{x^{2}+2}=\frac{x\left(3x+2\right)}{x^{2}+2}$$

Meta tiddividi b'x^{2}+2 titneħħa l-multiplikazzjoni b'x^{2}+2.

$$f=\frac{x\left(3x+2\right)}{x^{2}+2}$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{1+6f-2f^{2}}+1}{f-3}\text{, }&f\neq 0\text{ and }f\neq 3\\x=\frac{\sqrt{1+6f-2f^{2}}+1}{f-3}\text{, }&f\neq 3\\x=3\text{, }&f=3\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=\frac{-\sqrt{1+6f-2f^{2}}+1}{f-3}\text{, }&f\neq 3\text{ and }f\neq 0\text{ and }f\geq \frac{3-\sqrt{11}}{2}\text{ and }f\leq \frac{\sqrt{11}+3}{2}\\x=\frac{\sqrt{1+6f-2f^{2}}+1}{f-3}\text{, }&f\neq 3\text{ and }f\geq \frac{3-\sqrt{11}}{2}\text{ and }f\leq \frac{\sqrt{11}+3}{2}\\x=3\text{, }&f=3\end{matrix}\right.$$