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

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

Datrys ar gyfer x, y

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

Camau Ateb

Ystyriwch yr hafaliad cyntaf. Tynnu 117 o'r ddwy ochr. Mae tynnu unrhyw beth o sero’n rhoi negydd y swm.

$$-54x=-117$$

Rhannu’r ddwy ochr â -54.

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

Lleihau'r ffracsiwn \frac{-117}{-54} i'r graddau lleiaf posib drwy dynnu a chanslo allan -9.

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

Ystyriwch yr ail hafaliad. Mewnosod y gwerthoedd sy’n hysbys i’r hafaliad.

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

Cyfrifo \frac{13}{6} i bŵer 4 a chael \frac{28561}{1296}.

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

Cyfrifo \frac{13}{6} i bŵer 3 a chael \frac{2197}{216}.

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

Lluosi -6 a \frac{2197}{216} i gael -\frac{2197}{36}.

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

Tynnu \frac{2197}{36} o \frac{28561}{1296} i gael -\frac{50531}{1296}.

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

Cyfrifo \frac{13}{6} i bŵer 2 a chael \frac{169}{36}.

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

Lluosi 22 a \frac{169}{36} i gael \frac{1859}{18}.

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

Adio -\frac{50531}{1296} a \frac{1859}{18} i gael \frac{83317}{1296}.

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

Mae’r system wedi’i datrys nawr.

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