Réitigh x(2+16+24m^2-9m^4/2(3m^2+4))*2/m=frac{sqrt{6}}{2}*2

$$x ( 2 + \frac { 16 + 24 m ^ { 2 } - 9 m ^ { 4 } } { 2 ( 3 m ^ { 2 } + 4 ) } ) \times \frac { 2 } { m } = \frac { \sqrt { 6 } } { 2 } \times 2$$

Réitigh do x.

$$x=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}$$

$$m\neq 0\text{ and }|m|\neq \frac{\sqrt{6\sqrt{17}+18}}{3}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Iolraigh an dá thaobh den chothromóid faoi 2m\left(3m^{2}+4\right), an comhiolraí is lú de 2\left(3m^{2}+4\right),m,2.

$$x\left(2+\frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\right)\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh 2 faoi \frac{2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)}.

$$x\left(\frac{2\times 2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)}+\frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\right)\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Tá an t-ainmneoir céanna ag \frac{2\times 2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)} agus \frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$x\times \frac{2\times 2\left(3m^{2}+4\right)+16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Déan iolrúcháin in 2\times 2\left(3m^{2}+4\right)+16+24m^{2}-9m^{4}.

$$x\times \frac{12m^{2}+16+16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Cumaisc téarmaí comhchosúla in: 12m^{2}+16+16+24m^{2}-9m^{4}.

$$x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Scríobh x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)} mar chodán aonair.

$$\frac{x\left(36m^{2}+32-9m^{4}\right)}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Scríobh \frac{x\left(36m^{2}+32-9m^{4}\right)}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right) mar chodán aonair.

$$\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Scríobh \frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}\times 2 mar chodán aonair.

$$\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)\times 2}{2\left(3m^{2}+4\right)}=2m\left(3m^{2}+4\right)\sqrt{6}$$

Cealaigh 2 mar uimhreoir agus ainmneoir.

$$\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}=2m\left(3m^{2}+4\right)\sqrt{6}$$

Úsáid an t-airí dáileach chun 2m a mhéadú faoi 3m^{2}+4.

$$\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}=\left(6m^{3}+8m\right)\sqrt{6}$$

Úsáid an t-airí dáileach chun 6m^{3}+8m a mhéadú faoi \sqrt{6}.

$$\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}.

$$\frac{-2\times 9x\left(3m^{2}+4\right)\left(m^{2}-\left(-\frac{2}{3}\sqrt{17}+2\right)\right)\left(m^{2}-\left(\frac{2}{3}\sqrt{17}+2\right)\right)}{3m^{2}+4}=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Cealaigh 3m^{2}+4 mar uimhreoir agus ainmneoir.

$$-2\times 9x\left(m^{2}-\left(-\frac{2}{3}\sqrt{17}+2\right)\right)\left(m^{2}-\left(\frac{2}{3}\sqrt{17}+2\right)\right)=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Fairsingigh an slonn.

$$-18xm^{4}+72xm^{2}+64x=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Comhcheangail na téarmaí ar fad ina bhfuil x.

$$\left(-18m^{4}+72m^{2}+64\right)x=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(64+72m^{2}-18m^{4}\right)x=6\sqrt{6}m^{3}+8\sqrt{6}m$$

Roinn an dá thaobh faoi -18m^{4}+72m^{2}+64.

$$\frac{\left(64+72m^{2}-18m^{4}\right)x}{64+72m^{2}-18m^{4}}=\frac{2\sqrt{6}m\left(3m^{2}+4\right)}{64+72m^{2}-18m^{4}}$$

Má roinntear é faoi -18m^{4}+72m^{2}+64 cuirtear an iolrúchán faoi -18m^{4}+72m^{2}+64 ar ceal.

$$x=\frac{2\sqrt{6}m\left(3m^{2}+4\right)}{64+72m^{2}-18m^{4}}$$

Roinn 2m\left(3m^{2}+4\right)\sqrt{6} faoi -18m^{4}+72m^{2}+64.

$$x=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}$$