Issolvi {l}{f{(x)}=-6x+3}{g{(x)}=3x+21x^-3}{h=f{(-3)}}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { f {(x)} = -6 x + 3 }\\ { g {(x)} = 3 x + 21 x ^ {-3} }\\ { h = f {(-3)} }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Solvi għal f, x, g, h

$$x=\frac{162}{325}+\frac{9}{325}i\approx 0.498461538+0.027692308i$$

$$f=-\frac{1}{3}i\approx -0.333333333i$$

$$g=\frac{727792}{2187}-\frac{18088}{243}i\approx 332.780978509-74.436213992i$$

$$h=i$$

Passi tas-Soluzzjonijiet

Ikkunsidra r-raba' ekwazzjoni. Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$h=i$$

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

$$i=f\left(-3\right)$$

Iddividi ż-żewġ naħat b'-3.

$$\frac{i}{-3}=f$$

Iddividi i b'-3 biex tikseb-\frac{1}{3}i.

$$-\frac{1}{3}i=f$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$f=-\frac{1}{3}i$$

Ikkunsidra l-ewwel ekwazzjoni. Inserixxi l-valuri magħrufa tal-varjabbli fl-ekwazzjoni.

$$-\frac{1}{3}ix=-6x+3$$

Żid 6x maż-żewġ naħat.

$$-\frac{1}{3}ix+6x=3$$

Ikkombina -\frac{1}{3}ix u 6x biex tikseb \left(6-\frac{1}{3}i\right)x.

$$\left(6-\frac{1}{3}i\right)x=3$$

Iddividi ż-żewġ naħat b'6-\frac{1}{3}i.

$$x=\frac{3}{6-\frac{1}{3}i}$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{3}{6-\frac{1}{3}i} bil-konjugat kumpless tad-denominatur, 6+\frac{1}{3}i.

$$x=\frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}$$

Agħmel il-multiplikazzjonijiet fi \frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}.

$$x=\frac{18+i}{\frac{325}{9}}$$

Iddividi 18+i b'\frac{325}{9} biex tikseb\frac{162}{325}+\frac{9}{325}i.

$$x=\frac{162}{325}+\frac{9}{325}i$$

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

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=3\left(\frac{162}{325}+\frac{9}{325}i\right)+21\left(\frac{162}{325}+\frac{9}{325}i\right)^{-3}$$

Immultiplika 3 u \frac{162}{325}+\frac{9}{325}i biex tikseb \frac{486}{325}+\frac{27}{325}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+21\left(\frac{162}{325}+\frac{9}{325}i\right)^{-3}$$

Ikkalkula \frac{162}{325}+\frac{9}{325}i bil-power ta' -3 u tikseb \frac{214}{27}-\frac{971}{729}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+21\left(\frac{214}{27}-\frac{971}{729}i\right)$$

Immultiplika 21 u \frac{214}{27}-\frac{971}{729}i biex tikseb \frac{1498}{9}-\frac{6797}{243}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+\left(\frac{1498}{9}-\frac{6797}{243}i\right)$$

Żid \frac{486}{325}+\frac{27}{325}i u \frac{1498}{9}-\frac{6797}{243}i biex tikseb \frac{491224}{2925}-\frac{2202464}{78975}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{491224}{2925}-\frac{2202464}{78975}i$$

Iddividi ż-żewġ naħat b'\frac{162}{325}+\frac{9}{325}i.

$$g=\frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i}$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i} bil-konjugat kumpless tad-denominatur, \frac{162}{325}-\frac{9}{325}i.

$$g=\frac{\left(\frac{491224}{2925}-\frac{2202464}{78975}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}{\left(\frac{162}{325}+\frac{9}{325}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}$$

Agħmel il-multiplikazzjonijiet fi \frac{\left(\frac{491224}{2925}-\frac{2202464}{78975}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}{\left(\frac{162}{325}+\frac{9}{325}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}.

$$g=\frac{\frac{55984}{675}-\frac{18088}{975}i}{\frac{81}{325}}$$

Iddividi \frac{55984}{675}-\frac{18088}{975}i b'\frac{81}{325} biex tikseb\frac{727792}{2187}-\frac{18088}{243}i.

$$g=\frac{727792}{2187}-\frac{18088}{243}i$$

Is-sistema issa solvuta.

$$f=-\frac{1}{3}i x=\frac{162}{325}+\frac{9}{325}i g=\frac{727792}{2187}-\frac{18088}{243}i h=i$$