Whakaoti i te x+3/2=5/x+4

$$\frac { x + 3 } { 2 } = \frac { 5 } { x + 4 }$$

Whakaoti mō x

$$x=\frac{\sqrt{41}-7}{2}\approx -0.298437881$$

$$x=\frac{-\sqrt{41}-7}{2}\approx -6.701562119$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(x+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2,x+4.

$$\left(x+4\right)\left(x+3\right)=2\times 5$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+4 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}+7x+12=2\times 5$$

Whakareatia te 2 ki te 5, ka 10.

$$x^{2}+7x+12=10$$

Tangohia te 10 mai i ngā taha e rua.

$$x^{2}+7x+12-10=0$$

Tangohia te 10 i te 12, ka 2.

$$x^{2}+7x+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\times 2}}{2}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\times 2}}{2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-7±\sqrt{49-8}}{2}$$

Tāpiri 49 ki te -8.

$$x=\frac{-7±\sqrt{41}}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{41}}{2} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{41}.

$$x=\frac{\sqrt{41}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{41}}{2} ina he tango te ±. Tango \sqrt{41} mai i -7.

$$x=\frac{-\sqrt{41}-7}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{41}-7}{2} x=\frac{-\sqrt{41}-7}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(x+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2,x+4.

$$\left(x+4\right)\left(x+3\right)=2\times 5$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+4 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}+7x+12=2\times 5$$

Whakareatia te 2 ki te 5, ka 10.

$$x^{2}+7x+12=10$$

Tangohia te 12 mai i ngā taha e rua.

$$x^{2}+7x=10-12$$

Tangohia te 12 i te 10, ka -2.

$$x^{2}+7x=-2$$

Whakawehea te 7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{2}. Nā, tāpiria te pūrua o te \frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=-2+\left(\frac{7}{2}\right)^{2}$$

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+7x+\frac{49}{4}=-2+\frac{49}{4}$$

Tāpiri -2 ki te \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{41}{4}$$

Tauwehea x^{2}+7x+\frac{49}{4}. 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}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{41}{4}$$

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

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{41}{4}}$$

Whakarūnātia.

$$x+\frac{7}{2}=\frac{\sqrt{41}}{2} x+\frac{7}{2}=-\frac{\sqrt{41}}{2}$$

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{41}-7}{2} x=\frac{-\sqrt{41}-7}{2}$$