Whakaoti i te y^2+5y-7

$$y ^ { 2 } + 5 y - 7$$

Tauwehe

$$\left(y-\frac{-\sqrt{53}-5}{2}\right)\left(y-\frac{\sqrt{53}-5}{2}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$y^{2}+5y-7=0$$

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.

$$y=\frac{-5±\sqrt{5^{2}-4\left(-7\right)}}{2}$$

Pūrua 5.

$$y=\frac{-5±\sqrt{25-4\left(-7\right)}}{2}$$

Whakareatia -4 ki te -7.

$$y=\frac{-5±\sqrt{25+28}}{2}$$

Tāpiri 25 ki te 28.

$$y=\frac{-5±\sqrt{53}}{2}$$

Nā, me whakaoti te whārite y=\frac{-5±\sqrt{53}}{2} ina he tāpiri te ±. Tāpiri -5 ki te \sqrt{53}.

$$y=\frac{\sqrt{53}-5}{2}$$

Nā, me whakaoti te whārite y=\frac{-5±\sqrt{53}}{2} ina he tango te ±. Tango \sqrt{53} mai i -5.

$$y=\frac{-\sqrt{53}-5}{2}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{-5+\sqrt{53}}{2} mō te x_{1} me te \frac{-5-\sqrt{53}}{2} mō te x_{2}.

$$y^{2}+5y-7=\left(y-\frac{\sqrt{53}-5}{2}\right)\left(y-\frac{-\sqrt{53}-5}{2}\right)$$

Aromātai

$$y^{2}+5y-7$$