Whakaoti i te {l}{f{(x)}=20{(2x^3+3x^2-2x)}}{g=8x}{h=g}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { f {(x)} = 20 {(2 x ^ {3} + 3 x ^ {2} - 2 x)} }\\ { g = 8 x }\\ { h = g }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Whakaoti mō f, x, g, h

$$x=\frac{1}{8}i=0.125i$$

$$f=-\frac{325}{8}+\frac{15}{2}i=-40.625+7.5i$$

$$g=i$$

$$h=i$$

Ngā Upane Otinga

Whakaarohia te whārite tuawhā. Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$h=i$$

Whakaarohia te whārite tuatoru. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$i=g$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$g=i$$

Whakaarohia te whārite tuarua. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$i=8x$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{i}{8}=x$$

Whakawehea te i ki te 8, kia riro ko \frac{1}{8}i.

$$\frac{1}{8}i=x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x=\frac{1}{8}i$$

Whakaarohia te whārite tuatahi. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$f\times \left(\frac{1}{8}i\right)=20\left(2\times \left(\frac{1}{8}i\right)^{3}+3\times \left(\frac{1}{8}i\right)^{2}-2\times \left(\frac{1}{8}i\right)\right)$$

Tātaihia te \frac{1}{8}i mā te pū o 3, kia riro ko -\frac{1}{512}i.

$$f\times \left(\frac{1}{8}i\right)=20\left(2\times \left(-\frac{1}{512}i\right)+3\times \left(\frac{1}{8}i\right)^{2}-2\times \left(\frac{1}{8}i\right)\right)$$

Whakareatia te 2 ki te -\frac{1}{512}i, ka -\frac{1}{256}i.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i+3\times \left(\frac{1}{8}i\right)^{2}-2\times \left(\frac{1}{8}i\right)\right)$$

Tātaihia te \frac{1}{8}i mā te pū o 2, kia riro ko -\frac{1}{64}.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i+3\left(-\frac{1}{64}\right)-2\times \left(\frac{1}{8}i\right)\right)$$

Whakareatia te 3 ki te -\frac{1}{64}, ka -\frac{3}{64}.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i-\frac{3}{64}-2\times \left(\frac{1}{8}i\right)\right)$$

Whakareatia te -2 ki te \frac{1}{8}i, ka -\frac{1}{4}i.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{1}{256}i-\frac{3}{64}-\frac{1}{4}i\right)$$

Mahia ngā tāpiri i roto o -\frac{1}{256}i-\frac{3}{64}-\frac{1}{4}i.

$$f\times \left(\frac{1}{8}i\right)=20\left(-\frac{3}{64}-\frac{65}{256}i\right)$$

Whakareatia te 20 ki te -\frac{3}{64}-\frac{65}{256}i, ka -\frac{15}{16}-\frac{325}{64}i.

$$f\times \left(\frac{1}{8}i\right)=-\frac{15}{16}-\frac{325}{64}i$$

Whakawehea ngā taha e rua ki te \frac{1}{8}i.

$$f=\frac{-\frac{15}{16}-\frac{325}{64}i}{\frac{1}{8}i}$$

Me whakarea tahi te taurunga me te tauraro o \frac{-\frac{15}{16}-\frac{325}{64}i}{\frac{1}{8}i} ki te wae pohewa i.

$$f=\frac{\frac{325}{64}-\frac{15}{16}i}{-\frac{1}{8}}$$

Whakawehea te \frac{325}{64}-\frac{15}{16}i ki te -\frac{1}{8}, kia riro ko -\frac{325}{8}+\frac{15}{2}i.

$$f=-\frac{325}{8}+\frac{15}{2}i$$

Kua oti te pūnaha te whakatau.

$$f=-\frac{325}{8}+\frac{15}{2}i x=\frac{1}{8}i g=i h=i$$