Whakaoti i te 208/x+16+2=216/x

$$\frac { 208 } { x + 16 } + 2 = \frac { 216 } { x }$$

Whakaoti mō x

$$x=-48$$

$$x=36$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -16,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x+16\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+16,x.

$$x\times 208+x\left(x+16\right)\times 2=\left(x+16\right)\times 216$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+16.

$$x\times 208+\left(x^{2}+16x\right)\times 2=\left(x+16\right)\times 216$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+16x ki te 2.

$$x\times 208+2x^{2}+32x=\left(x+16\right)\times 216$$

Pahekotia te x\times 208 me 32x, ka 240x.

$$240x+2x^{2}=\left(x+16\right)\times 216$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+16 ki te 216.

$$240x+2x^{2}=216x+3456$$

Tangohia te 216x mai i ngā taha e rua.

$$240x+2x^{2}-216x=3456$$

Pahekotia te 240x me -216x, ka 24x.

$$24x+2x^{2}=3456$$

Tangohia te 3456 mai i ngā taha e rua.

$$24x+2x^{2}-3456=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$2x^{2}+24x-3456=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 24 mō b, me -3456 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-24±\sqrt{24^{2}-4\times 2\left(-3456\right)}}{2\times 2}$$

Pūrua 24.

$$x=\frac{-24±\sqrt{576-4\times 2\left(-3456\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-24±\sqrt{576-8\left(-3456\right)}}{2\times 2}$$

Whakareatia -8 ki te -3456.

$$x=\frac{-24±\sqrt{576+27648}}{2\times 2}$$

Tāpiri 576 ki te 27648.

$$x=\frac{-24±\sqrt{28224}}{2\times 2}$$

Tuhia te pūtakerua o te 28224.

$$x=\frac{-24±168}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-24±168}{4}$$

Nā, me whakaoti te whārite x=\frac{-24±168}{4} ina he tāpiri te ±. Tāpiri -24 ki te 168.

$$x=\frac{144}{4}$$

Whakawehe 144 ki te 4.

$$x=36$$

Nā, me whakaoti te whārite x=\frac{-24±168}{4} ina he tango te ±. Tango 168 mai i -24.

$$x=-\frac{192}{4}$$

Whakawehe -192 ki te 4.

$$x=-48$$

Kua oti te whārite te whakatau.

$$x=36 x=-48$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -16,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x+16\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+16,x.

$$x\times 208+x\left(x+16\right)\times 2=\left(x+16\right)\times 216$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+16.

$$x\times 208+\left(x^{2}+16x\right)\times 2=\left(x+16\right)\times 216$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+16x ki te 2.

$$x\times 208+2x^{2}+32x=\left(x+16\right)\times 216$$

Pahekotia te x\times 208 me 32x, ka 240x.

$$240x+2x^{2}=\left(x+16\right)\times 216$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+16 ki te 216.

$$240x+2x^{2}=216x+3456$$

Tangohia te 216x mai i ngā taha e rua.

$$240x+2x^{2}-216x=3456$$

Pahekotia te 240x me -216x, ka 24x.

$$24x+2x^{2}=3456$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$2x^{2}+24x=3456$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+24x}{2}=\frac{3456}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{24}{2}x=\frac{3456}{2}$$

Whakawehe 24 ki te 2.

$$x^{2}+12x=\frac{3456}{2}$$

Whakawehe 3456 ki te 2.

$$x^{2}+12x=1728$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+12x+6^{2}=1728+6^{2}$$

Pūrua 6.

$$x^{2}+12x+36=1728+36$$

Tāpiri 1728 ki te 36.

$$x^{2}+12x+36=1764$$

Tauwehea x^{2}+12x+36. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+6\right)^{2}=1764$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{1764}$$

Whakarūnātia.

$$x+6=42 x+6=-42$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=36 x=-48$$