Whakaoti i te HB=1500/314*5*(5-sqrt{5^2-2295^2)}

$$H B = \frac { 1500 } { 314 \cdot 5 \cdot ( 5 - \sqrt { 5 ^ { 2 } - 2295 ^ { 2 } } ) }$$

Whakaoti mō B

$$B=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639H}$$

$$H\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 5 ki te 314, ka 1570.

$$HB=\frac{1500}{1570\left(5-\sqrt{5^{2}-2295^{2}}\right)}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-2295^{2}}\right)}$$

Tātaihia te 2295 mā te pū o 2, kia riro ko 5267025.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-5267025}\right)}$$

Tangohia te 5267025 i te 25, ka -5267000.

$$HB=\frac{1500}{1570\left(5-\sqrt{-5267000}\right)}$$

Tauwehea te -5267000=\left(10i\right)^{2}\times 52670. Tuhia anō te pūtake rua o te hua \sqrt{\left(10i\right)^{2}\times 52670} hei hua o ngā pūtake rua \sqrt{\left(10i\right)^{2}}\sqrt{52670}. Tuhia te pūtakerua o te \left(10i\right)^{2}.

$$HB=\frac{1500}{1570\left(5-10i\sqrt{52670}\right)}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1570 ki te 5-10i\sqrt{52670}.

$$HB=\frac{1500}{7850-15700i\sqrt{52670}}$$

Whakangāwaritia te tauraro o \frac{1500}{7850-15700i\sqrt{52670}} mā te whakarea i te taurunga me te tauraro ki te 7850+15700i\sqrt{52670}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{\left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right)}$$

Whakaarohia te \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{7850^{2}-\left(-15700i\sqrt{52670}\right)^{2}}$$

Tātaihia te 7850 mā te pū o 2, kia riro ko 61622500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\sqrt{52670}\right)^{2}}$$

Whakarohaina te \left(-15700i\sqrt{52670}\right)^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\right)^{2}\left(\sqrt{52670}\right)^{2}}$$

Tātaihia te -15700i mā te pū o 2, kia riro ko -246490000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\left(\sqrt{52670}\right)^{2}\right)}$$

Ko te pūrua o \sqrt{52670} ko 52670.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\times 52670\right)}$$

Whakareatia te -246490000 ki te 52670, ka -12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-12982628300000\right)}$$

Whakareatia te -1 ki te -12982628300000, ka 12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500+12982628300000}$$

Tāpirihia te 61622500 ki te 12982628300000, ka 12982689922500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{12982689922500}$$

Whakawehea te 1500\left(7850+15700i\sqrt{52670}\right) ki te 12982689922500, kia riro ko \frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right).

$$HB=\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{8655126615} ki te 7850+15700i\sqrt{52670}.

$$HB=\frac{10}{11025639}+\frac{20}{11025639}i\sqrt{52670}$$

Whakaraupapatia anō ngā kīanga tau.

$$BH=\frac{10}{11025639}+\frac{20}{11025639}\sqrt{52670}i$$

He hanga arowhānui tō te whārite.

$$HB=\frac{10+20\sqrt{52670}i}{11025639}$$

Whakawehea ngā taha e rua ki te H.

$$\frac{HB}{H}=\frac{10+20\sqrt{52670}i}{11025639H}$$

Mā te whakawehe ki te H ka wetekia te whakareanga ki te H.

$$B=\frac{10+20\sqrt{52670}i}{11025639H}$$

Whakawehe \frac{10+20i\sqrt{52670}}{11025639} ki te H.

$$B=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639H}$$

Whakaoti mō H

$$H=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639B}$$

$$B\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 5 ki te 314, ka 1570.

$$HB=\frac{1500}{1570\left(5-\sqrt{5^{2}-2295^{2}}\right)}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-2295^{2}}\right)}$$

Tātaihia te 2295 mā te pū o 2, kia riro ko 5267025.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-5267025}\right)}$$

Tangohia te 5267025 i te 25, ka -5267000.

$$HB=\frac{1500}{1570\left(5-\sqrt{-5267000}\right)}$$

Tauwehea te -5267000=\left(10i\right)^{2}\times 52670. Tuhia anō te pūtake rua o te hua \sqrt{\left(10i\right)^{2}\times 52670} hei hua o ngā pūtake rua \sqrt{\left(10i\right)^{2}}\sqrt{52670}. Tuhia te pūtakerua o te \left(10i\right)^{2}.

$$HB=\frac{1500}{1570\left(5-10i\sqrt{52670}\right)}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1570 ki te 5-10i\sqrt{52670}.

$$HB=\frac{1500}{7850-15700i\sqrt{52670}}$$

Whakangāwaritia te tauraro o \frac{1500}{7850-15700i\sqrt{52670}} mā te whakarea i te taurunga me te tauraro ki te 7850+15700i\sqrt{52670}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{\left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right)}$$

Whakaarohia te \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{7850^{2}-\left(-15700i\sqrt{52670}\right)^{2}}$$

Tātaihia te 7850 mā te pū o 2, kia riro ko 61622500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\sqrt{52670}\right)^{2}}$$

Whakarohaina te \left(-15700i\sqrt{52670}\right)^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\right)^{2}\left(\sqrt{52670}\right)^{2}}$$

Tātaihia te -15700i mā te pū o 2, kia riro ko -246490000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\left(\sqrt{52670}\right)^{2}\right)}$$

Ko te pūrua o \sqrt{52670} ko 52670.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\times 52670\right)}$$

Whakareatia te -246490000 ki te 52670, ka -12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-12982628300000\right)}$$

Whakareatia te -1 ki te -12982628300000, ka 12982628300000.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500+12982628300000}$$

Tāpirihia te 61622500 ki te 12982628300000, ka 12982689922500.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{12982689922500}$$

Whakawehea te 1500\left(7850+15700i\sqrt{52670}\right) ki te 12982689922500, kia riro ko \frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right).

$$HB=\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{8655126615} ki te 7850+15700i\sqrt{52670}.

$$HB=\frac{10}{11025639}+\frac{20}{11025639}i\sqrt{52670}$$

Whakaraupapatia anō ngā kīanga tau.

$$BH=\frac{10}{11025639}+\frac{20}{11025639}\sqrt{52670}i$$

He hanga arowhānui tō te whārite.

$$BH=\frac{10+20\sqrt{52670}i}{11025639}$$

Whakawehea ngā taha e rua ki te B.

$$\frac{BH}{B}=\frac{10+20\sqrt{52670}i}{11025639B}$$

Mā te whakawehe ki te B ka wetekia te whakareanga ki te B.

$$H=\frac{10+20\sqrt{52670}i}{11025639B}$$

Whakawehe \frac{10+20i\sqrt{52670}}{11025639} ki te B.

$$H=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639B}$$