Whakaoti i te y^2+4y+8y-12=0

$$y ^ { 2 } + 4 y + 8 y - 12 = 0$$

Whakaoti mō y

$$y=4\sqrt{3}-6\approx 0.92820323$$

$$y=-4\sqrt{3}-6\approx -12.92820323$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 4y me 8y, ka 12y.

$$y^{2}+12y-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-12±\sqrt{12^{2}-4\left(-12\right)}}{2}$$

Pūrua 12.

$$y=\frac{-12±\sqrt{144-4\left(-12\right)}}{2}$$

Whakareatia -4 ki te -12.

$$y=\frac{-12±\sqrt{144+48}}{2}$$

Tāpiri 144 ki te 48.

$$y=\frac{-12±\sqrt{192}}{2}$$

Tuhia te pūtakerua o te 192.

$$y=\frac{-12±8\sqrt{3}}{2}$$

Nā, me whakaoti te whārite y=\frac{-12±8\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 8\sqrt{3}.

$$y=\frac{8\sqrt{3}-12}{2}$$

Whakawehe -12+8\sqrt{3} ki te 2.

$$y=4\sqrt{3}-6$$

Nā, me whakaoti te whārite y=\frac{-12±8\sqrt{3}}{2} ina he tango te ±. Tango 8\sqrt{3} mai i -12.

$$y=\frac{-8\sqrt{3}-12}{2}$$

Whakawehe -12-8\sqrt{3} ki te 2.

$$y=-4\sqrt{3}-6$$

Kua oti te whārite te whakatau.

$$y=4\sqrt{3}-6 y=-4\sqrt{3}-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 4y me 8y, ka 12y.

$$y^{2}+12y-12=0$$

Me tāpiri te 12 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$y^{2}+12y=12$$

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.

$$y^{2}+12y+6^{2}=12+6^{2}$$

Pūrua 6.

$$y^{2}+12y+36=12+36$$

Tāpiri 12 ki te 36.

$$y^{2}+12y+36=48$$

Tauwehea y^{2}+12y+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}.

$$\left(y+6\right)^{2}=48$$

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

$$\sqrt{\left(y+6\right)^{2}}=\sqrt{48}$$

Whakarūnātia.

$$y+6=4\sqrt{3} y+6=-4\sqrt{3}$$

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

$$y=4\sqrt{3}-6 y=-4\sqrt{3}-6$$