Réitigh n^2-8=113?quadn^2-105

$$n ^ { 2 } - 8 = 113 ? \quad n ^ { 2 } - 105$$

Réitigh do n.

$$n=\frac{\sqrt{679}}{28}\approx 0.930629587$$

$$n=-\frac{\sqrt{679}}{28}\approx -0.930629587$$

Céimeanna tríd an bhFréamh Chearnach a Fháil

Bain 113n^{2} ón dá thaobh.

$$n^{2}-8-113n^{2}=-105$$

Comhcheangail n^{2} agus -113n^{2} chun -112n^{2} a fháil.

$$-112n^{2}-8=-105$$

Cuir 8 leis an dá thaobh.

$$-112n^{2}=-105+8$$

Suimigh -105 agus 8 chun -97 a fháil.

$$-112n^{2}=-97$$

Roinn an dá thaobh faoi -112.

$$n^{2}=\frac{-97}{-112}$$

Is féidir an codán \frac{-97}{-112} a shimpliú mar \frac{97}{112} ach an comhartha diúltach a bhaint den uimhreoir agus den ainmneoir.

$$n^{2}=\frac{97}{112}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$n=\frac{\sqrt{679}}{28} n=-\frac{\sqrt{679}}{28}$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Bain 113n^{2} ón dá thaobh.

$$n^{2}-8-113n^{2}=-105$$

Comhcheangail n^{2} agus -113n^{2} chun -112n^{2} a fháil.

$$-112n^{2}-8=-105$$

Cuir 105 leis an dá thaobh.

$$-112n^{2}-8+105=0$$

Suimigh -8 agus 105 chun 97 a fháil.

$$-112n^{2}+97=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -112 in ionad a, 0 in ionad b, agus 97 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-112\right)\times 97}}{2\left(-112\right)}$$

Cearnóg 0.

$$n=\frac{0±\sqrt{-4\left(-112\right)\times 97}}{2\left(-112\right)}$$

Méadaigh -4 faoi -112.

$$n=\frac{0±\sqrt{448\times 97}}{2\left(-112\right)}$$

Méadaigh 448 faoi 97.

$$n=\frac{0±\sqrt{43456}}{2\left(-112\right)}$$

Tóg fréamh chearnach 43456.

$$n=\frac{0±8\sqrt{679}}{2\left(-112\right)}$$

Méadaigh 2 faoi -112.

$$n=\frac{0±8\sqrt{679}}{-224}$$

Réitigh an chothromóid n=\frac{0±8\sqrt{679}}{-224} nuair is ionann ± agus plus.

$$n=-\frac{\sqrt{679}}{28}$$

Réitigh an chothromóid n=\frac{0±8\sqrt{679}}{-224} nuair is ionann ± agus míneas.

$$n=\frac{\sqrt{679}}{28}$$

Tá an chothromóid réitithe anois.

$$n=-\frac{\sqrt{679}}{28} n=\frac{\sqrt{679}}{28}$$