Whakaoti i te 64*6=25*15(x^2+1)

$$64 \times 6 = 25 \times 15 ( x ^ { 2 } + 1 )$$

Whakaoti mō x

$$x=\frac{\sqrt{15}}{25}\approx 0.154919334$$

$$x=-\frac{\sqrt{15}}{25}\approx -0.154919334$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 64 ki te 6, ka 384.

$$384=25\times 15\left(x^{2}+1\right)$$

Whakareatia te 25 ki te 15, ka 375.

$$384=375\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 375 ki te x^{2}+1.

$$384=375x^{2}+375$$

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

$$375x^{2}+375=384$$

Tangohia te 375 mai i ngā taha e rua.

$$375x^{2}=384-375$$

Tangohia te 375 i te 384, ka 9.

$$375x^{2}=9$$

Whakawehea ngā taha e rua ki te 375.

$$x^{2}=\frac{9}{375}$$

Whakahekea te hautanga \frac{9}{375} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x^{2}=\frac{3}{125}$$

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

$$x=\frac{\sqrt{15}}{25} x=-\frac{\sqrt{15}}{25}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 64 ki te 6, ka 384.

$$384=25\times 15\left(x^{2}+1\right)$$

Whakareatia te 25 ki te 15, ka 375.

$$384=375\left(x^{2}+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 375 ki te x^{2}+1.

$$384=375x^{2}+375$$

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

$$375x^{2}+375=384$$

Tangohia te 384 mai i ngā taha e rua.

$$375x^{2}+375-384=0$$

Tangohia te 384 i te 375, ka -9.

$$375x^{2}-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 375 mō a, 0 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 375\left(-9\right)}}{2\times 375}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 375\left(-9\right)}}{2\times 375}$$

Whakareatia -4 ki te 375.

$$x=\frac{0±\sqrt{-1500\left(-9\right)}}{2\times 375}$$

Whakareatia -1500 ki te -9.

$$x=\frac{0±\sqrt{13500}}{2\times 375}$$

Tuhia te pūtakerua o te 13500.

$$x=\frac{0±30\sqrt{15}}{2\times 375}$$

Whakareatia 2 ki te 375.

$$x=\frac{0±30\sqrt{15}}{750}$$

Nā, me whakaoti te whārite x=\frac{0±30\sqrt{15}}{750} ina he tāpiri te ±.

$$x=\frac{\sqrt{15}}{25}$$

Nā, me whakaoti te whārite x=\frac{0±30\sqrt{15}}{750} ina he tango te ±.

$$x=-\frac{\sqrt{15}}{25}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{15}}{25} x=-\frac{\sqrt{15}}{25}$$