Issolvi (5sqrt{2}-e)(3sqrt{2}+e)=fsqrt{2}-6

$$( 5 \sqrt { 2 } - e ) ( 3 \sqrt { 2 } + e ) = f \sqrt { 2 } - 6$$

Solvi għal f

$$f=-\frac{\sqrt{2}e^{2}}{2}+2e+18\sqrt{2}\approx 25.667556106$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 5\sqrt{2}-e b'kull terminu ta' 3\sqrt{2}+e.

$$15\left(\sqrt{2}\right)^{2}+5\sqrt{2}e-3e\sqrt{2}-e^{2}=f\sqrt{2}-6$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$15\times 2+5\sqrt{2}e-3e\sqrt{2}-e^{2}=f\sqrt{2}-6$$

Immultiplika 15 u 2 biex tikseb 30.

$$30+5\sqrt{2}e-3e\sqrt{2}-e^{2}=f\sqrt{2}-6$$

Ikkombina 5\sqrt{2}e u -3e\sqrt{2} biex tikseb 2\sqrt{2}e.

$$30+2\sqrt{2}e-e^{2}=f\sqrt{2}-6$$

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

$$f\sqrt{2}-6=30+2\sqrt{2}e-e^{2}$$

Żid 6 maż-żewġ naħat.

$$f\sqrt{2}=30+2\sqrt{2}e-e^{2}+6$$

Żid 30 u 6 biex tikseb 36.

$$f\sqrt{2}=36+2\sqrt{2}e-e^{2}$$

L-ekwazzjoni hija f'forma standard.

$$\sqrt{2}f=2e\sqrt{2}-e^{2}+36$$

Iddividi ż-żewġ naħat b'\sqrt{2}.

$$\frac{\sqrt{2}f}{\sqrt{2}}=\frac{2e\sqrt{2}-e^{2}+36}{\sqrt{2}}$$

Meta tiddividi b'\sqrt{2} titneħħa l-multiplikazzjoni b'\sqrt{2}.

$$f=\frac{2e\sqrt{2}-e^{2}+36}{\sqrt{2}}$$

Iddividi 36+2e\sqrt{2}-e^{2} b'\sqrt{2}.

$$f=\frac{\sqrt{2}\left(2e\sqrt{2}-e^{2}+36\right)}{2}$$