Réitigh q=sqrt{L}+sqrt{8}

$$q = \sqrt { L } + \sqrt { 8 }$$

Réitigh do L.

$$L=\left(q-2\sqrt{2}\right)^{2}$$

$$q-2\sqrt{2}\geq 0$$

Céimeanna chun cothromóidí fréimhe a réiteach

Fachtóirigh 8=2^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{2}. Tóg fréamh chearnach 2^{2}.

$$q=\sqrt{L}+2\sqrt{2}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$\sqrt{L}+2\sqrt{2}=q$$

Bain 2\sqrt{2} ón dá thaobh.

$$\sqrt{L}=q-2\sqrt{2}$$

Cearnaigh an dá thaobh den chothromóid.

$$L=\left(q-2\sqrt{2}\right)^{2}$$

Réitigh do L. (complex solution)

$$L=\left(q-2\sqrt{2}\right)^{2}$$

$$q=2\sqrt{2}\text{ or }arg(q-2\sqrt{2})<\pi$$

Réitigh do q. (complex solution)

$$q=\sqrt{L}+2\sqrt{2}$$

Réitigh do q.

$$q=\sqrt{L}+2\sqrt{2}$$

$$L\geq 0$$