Whakaoti i te (85-30)(85+36)/(85-b)(85+b)=11/20

$$\frac { ( 85 - 30 ) ( 85 + 36 ) } { ( 85 - b ) ( 85 + b ) } = \frac { 11 } { 20 }$$

Whakaoti mō b

$$b=-5\sqrt{195}i\approx -0-69.821200219i$$

$$b=5\sqrt{195}i\approx 69.821200219i$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe b ki tētahi o ngā uara -85,85 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20\left(b-85\right)\left(b+85\right), arā, te tauraro pātahi he tino iti rawa te kitea o \left(85-b\right)\left(85+b\right),20.

$$-20\left(85-30\right)\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Tangohia te 30 i te 85, ka 55.

$$-20\times 55\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Whakareatia te -20 ki te 55, ka -1100.

$$-1100\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Tāpirihia te 85 ki te 36, ka 121.

$$-1100\times 121=11\left(b-85\right)\left(b+85\right)$$

Whakareatia te -1100 ki te 121, ka -133100.

$$-133100=11\left(b-85\right)\left(b+85\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 11 ki te b-85.

$$-133100=\left(11b-935\right)\left(b+85\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 11b-935 ki te b+85 ka whakakotahi i ngā kupu rite.

$$-133100=11b^{2}-79475$$

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

$$11b^{2}-79475=-133100$$

Me tāpiri te 79475 ki ngā taha e rua.

$$11b^{2}=-133100+79475$$

Tāpirihia te -133100 ki te 79475, ka -53625.

$$11b^{2}=-53625$$

Whakawehea ngā taha e rua ki te 11.

$$b^{2}=\frac{-53625}{11}$$

Whakawehea te -53625 ki te 11, kia riro ko -4875.

$$b^{2}=-4875$$

Kua oti te whārite te whakatau.

$$b=5\sqrt{195}i b=-5\sqrt{195}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe b ki tētahi o ngā uara -85,85 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20\left(b-85\right)\left(b+85\right), arā, te tauraro pātahi he tino iti rawa te kitea o \left(85-b\right)\left(85+b\right),20.

$$-20\left(85-30\right)\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Tangohia te 30 i te 85, ka 55.

$$-20\times 55\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Whakareatia te -20 ki te 55, ka -1100.

$$-1100\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Tāpirihia te 85 ki te 36, ka 121.

$$-1100\times 121=11\left(b-85\right)\left(b+85\right)$$

Whakareatia te -1100 ki te 121, ka -133100.

$$-133100=11\left(b-85\right)\left(b+85\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 11 ki te b-85.

$$-133100=\left(11b-935\right)\left(b+85\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 11b-935 ki te b+85 ka whakakotahi i ngā kupu rite.

$$-133100=11b^{2}-79475$$

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

$$11b^{2}-79475=-133100$$

Me tāpiri te 133100 ki ngā taha e rua.

$$11b^{2}-79475+133100=0$$

Tāpirihia te -79475 ki te 133100, ka 53625.

$$11b^{2}+53625=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 11 mō a, 0 mō b, me 53625 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 11\times 53625}}{2\times 11}$$

Pūrua 0.

$$b=\frac{0±\sqrt{-4\times 11\times 53625}}{2\times 11}$$

Whakareatia -4 ki te 11.

$$b=\frac{0±\sqrt{-44\times 53625}}{2\times 11}$$

Whakareatia -44 ki te 53625.

$$b=\frac{0±\sqrt{-2359500}}{2\times 11}$$

Tuhia te pūtakerua o te -2359500.

$$b=\frac{0±110\sqrt{195}i}{2\times 11}$$

Whakareatia 2 ki te 11.

$$b=\frac{0±110\sqrt{195}i}{22}$$

Nā, me whakaoti te whārite b=\frac{0±110\sqrt{195}i}{22} ina he tāpiri te ±.

$$b=5\sqrt{195}i$$

Nā, me whakaoti te whārite b=\frac{0±110\sqrt{195}i}{22} ina he tango te ±.

$$b=-5\sqrt{195}i$$

Kua oti te whārite te whakatau.

$$b=5\sqrt{195}i b=-5\sqrt{195}i$$