Whakaoti i te 2=-5*12+11+11*3+a/sqrt{12^2+11^2+1}

$$2 = \frac{ -5 \times 12+11+11 \times 3+a }{ \sqrt{ { 12 }^{ 2 } + { 11 }^{ 2 } +1 } }$$

Whakaoti mō a

$$a=2\left(\sqrt{266}+8\right)\approx 48.619012861$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te -5 ki te 12, ka -60. Whakareatia te 11 ki te 3, ka 33.

$$2=\frac{-60+11+33+a}{\sqrt{12^{2}+11^{2}+1}}$$

Tāpirihia te -60 ki te 11, ka -49.

$$2=\frac{-49+33+a}{\sqrt{12^{2}+11^{2}+1}}$$

Tāpirihia te -49 ki te 33, ka -16.

$$2=\frac{-16+a}{\sqrt{12^{2}+11^{2}+1}}$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$2=\frac{-16+a}{\sqrt{144+11^{2}+1}}$$

Tātaihia te 11 mā te pū o 2, kia riro ko 121.

$$2=\frac{-16+a}{\sqrt{144+121+1}}$$

Tāpirihia te 144 ki te 121, ka 265.

$$2=\frac{-16+a}{\sqrt{265+1}}$$

Tāpirihia te 265 ki te 1, ka 266.

$$2=\frac{-16+a}{\sqrt{266}}$$

Whakangāwaritia te tauraro o \frac{-16+a}{\sqrt{266}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{266}.

$$2=\frac{\left(-16+a\right)\sqrt{266}}{\left(\sqrt{266}\right)^{2}}$$

Ko te pūrua o \sqrt{266} ko 266.

$$2=\frac{\left(-16+a\right)\sqrt{266}}{266}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -16+a ki te \sqrt{266}.

$$2=\frac{-16\sqrt{266}+a\sqrt{266}}{266}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{-16\sqrt{266}+a\sqrt{266}}{266}=2$$

Me whakarea ngā taha e rua ki te 266.

$$-16\sqrt{266}+a\sqrt{266}=2\times 266$$

Whakareatia te 2 ki te 266, ka 532.

$$-16\sqrt{266}+a\sqrt{266}=532$$

Me tāpiri te 16\sqrt{266} ki ngā taha e rua.

$$a\sqrt{266}=532+16\sqrt{266}$$

He hanga arowhānui tō te whārite.

$$\sqrt{266}a=16\sqrt{266}+532$$

Whakawehea ngā taha e rua ki te \sqrt{266}.

$$\frac{\sqrt{266}a}{\sqrt{266}}=\frac{16\sqrt{266}+532}{\sqrt{266}}$$

Mā te whakawehe ki te \sqrt{266} ka wetekia te whakareanga ki te \sqrt{266}.

$$a=\frac{16\sqrt{266}+532}{\sqrt{266}}$$

Whakawehe 532+16\sqrt{266} ki te \sqrt{266}.

$$a=2\sqrt{266}+16$$