Whakaoti i te 132(x^2-1)=x^2+7

$$132 ( x ^ { 2 } - 1 ) = x ^ { 2 } + 7$$

Whakaoti mō x

$$x = \frac{\sqrt{18209}}{131} \approx 1.030081891$$

$$x = -\frac{\sqrt{18209}}{131} \approx -1.030081891$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te āhuatanga tohatoha hei whakarea te 132 ki te x^{2}-1.

$$132x^{2}-132=x^{2}+7$$

Tangohia te x^{2} mai i ngā taha e rua.

$$132x^{2}-132-x^{2}=7$$

Pahekotia te 132x^{2} me -x^{2}, ka 131x^{2}.

$$131x^{2}-132=7$$

Me tāpiri te 132 ki ngā taha e rua.

$$131x^{2}=7+132$$

Tāpirihia te 7 ki te 132, ka 139.

$$131x^{2}=139$$

Whakawehea ngā taha e rua ki te 131.

$$x^{2}=\frac{139}{131}$$

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

$$x=\frac{\sqrt{18209}}{131} x=-\frac{\sqrt{18209}}{131}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 132 ki te x^{2}-1.

$$132x^{2}-132=x^{2}+7$$

Tangohia te x^{2} mai i ngā taha e rua.

$$132x^{2}-132-x^{2}=7$$

Pahekotia te 132x^{2} me -x^{2}, ka 131x^{2}.

$$131x^{2}-132=7$$

Tangohia te 7 mai i ngā taha e rua.

$$131x^{2}-132-7=0$$

Tangohia te 7 i te -132, ka -139.

$$131x^{2}-139=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 131 mō a, 0 mō b, me -139 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 131\left(-139\right)}}{2\times 131}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 131\left(-139\right)}}{2\times 131}$$

Whakareatia -4 ki te 131.

$$x=\frac{0±\sqrt{-524\left(-139\right)}}{2\times 131}$$

Whakareatia -524 ki te -139.

$$x=\frac{0±\sqrt{72836}}{2\times 131}$$

Tuhia te pūtakerua o te 72836.

$$x=\frac{0±2\sqrt{18209}}{2\times 131}$$

Whakareatia 2 ki te 131.

$$x=\frac{0±2\sqrt{18209}}{262}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{18209}}{262} ina he tāpiri te ±.

$$x=\frac{\sqrt{18209}}{131}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{18209}}{262} ina he tango te ±.

$$x=-\frac{\sqrt{18209}}{131}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{18209}}{131} x=-\frac{\sqrt{18209}}{131}$$