Whakaoti i te {l}{-54x+117=0}{text{Solvefor}ytext{where}}{y=x^4-6x^3+22x^2}

$$\left. \begin{array} { l } { -54 x + 117 = 0 }\\ { \text{Solve for } y \text{ where} } \\ { y = x ^ {4} - 6 x ^ {3} + 22 x ^ {2} } \end{array} \right.$$

Whakaoti mō x, y

$$y = \frac{83317}{1296} = 64\frac{373}{1296} \approx 64.287808642$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Tangohia te 117 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-54x=-117$$

Whakawehea ngā taha e rua ki te -54.

$$x=\frac{-117}{-54}$$

Whakahekea te hautanga \frac{-117}{-54} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -9.

$$x=\frac{13}{6}$$

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

$$y=\left(\frac{13}{6}\right)^{4}-6\times \left(\frac{13}{6}\right)^{3}+22\times \left(\frac{13}{6}\right)^{2}$$

Tātaihia te \frac{13}{6} mā te pū o 4, kia riro ko \frac{28561}{1296}.

$$y=\frac{28561}{1296}-6\times \left(\frac{13}{6}\right)^{3}+22\times \left(\frac{13}{6}\right)^{2}$$

Tātaihia te \frac{13}{6} mā te pū o 3, kia riro ko \frac{2197}{216}.

$$y=\frac{28561}{1296}-6\times \frac{2197}{216}+22\times \left(\frac{13}{6}\right)^{2}$$

Whakareatia te -6 ki te \frac{2197}{216}, ka -\frac{2197}{36}.

$$y=\frac{28561}{1296}-\frac{2197}{36}+22\times \left(\frac{13}{6}\right)^{2}$$

Tangohia te \frac{2197}{36} i te \frac{28561}{1296}, ka -\frac{50531}{1296}.

$$y=-\frac{50531}{1296}+22\times \left(\frac{13}{6}\right)^{2}$$

Tātaihia te \frac{13}{6} mā te pū o 2, kia riro ko \frac{169}{36}.

$$y=-\frac{50531}{1296}+22\times \frac{169}{36}$$

Whakareatia te 22 ki te \frac{169}{36}, ka \frac{1859}{18}.

$$y=-\frac{50531}{1296}+\frac{1859}{18}$$

Tāpirihia te -\frac{50531}{1296} ki te \frac{1859}{18}, ka \frac{83317}{1296}.

$$y=\frac{83317}{1296}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{13}{6} y=\frac{83317}{1296}$$