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

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

Solvi għal x, y

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

Passi tas-Soluzzjonijiet

Ikkunsidra l-ewwel ekwazzjoni. Naqqas 117 miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$-54x=-117$$

Iddividi ż-żewġ naħat b'-54.

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

Naqqas il-frazzjoni \frac{-117}{-54} għat-termini l-aktar baxxi billi testratta u tikkanċella barra -9.

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

Ikkunsidra t-tieni ekwazzjoni. Inserixxi l-valuri magħrufa tal-varjabbli fl-ekwazzjoni.

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

Ikkalkula \frac{13}{6} bil-power ta' 4 u tikseb \frac{28561}{1296}.

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

Ikkalkula \frac{13}{6} bil-power ta' 3 u tikseb \frac{2197}{216}.

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

Immultiplika -6 u \frac{2197}{216} biex tikseb -\frac{2197}{36}.

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

Naqqas \frac{2197}{36} minn \frac{28561}{1296} biex tikseb -\frac{50531}{1296}.

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

Ikkalkula \frac{13}{6} bil-power ta' 2 u tikseb \frac{169}{36}.

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

Immultiplika 22 u \frac{169}{36} biex tikseb \frac{1859}{18}.

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

Żid -\frac{50531}{1296} u \frac{1859}{18} biex tikseb \frac{83317}{1296}.

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

Is-sistema issa solvuta.

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