Whakaoti i te (2020+2022+2023+2024+2025+2033+2039)div13=xx...y

$$(2020+2022+2023+2024+2025+2033+2039) \div 13=xx...y$$

Whakaoti mō x

$$x = \frac{\sqrt{184418}}{13} \approx 33.033782242$$

$$x = -\frac{\sqrt{184418}}{13} \approx -33.033782242$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 13.

$$2020+2022+2023+2024+2025+2033+2039=13xx$$

Whakareatia te x ki te x, ka x^{2}.

$$2020+2022+2023+2024+2025+2033+2039=13x^{2}$$

Tāpirihia te 2020 ki te 2022, ka 4042.

$$4042+2023+2024+2025+2033+2039=13x^{2}$$

Tāpirihia te 4042 ki te 2023, ka 6065.

$$6065+2024+2025+2033+2039=13x^{2}$$

Tāpirihia te 6065 ki te 2024, ka 8089.

$$8089+2025+2033+2039=13x^{2}$$

Tāpirihia te 8089 ki te 2025, ka 10114.

$$10114+2033+2039=13x^{2}$$

Tāpirihia te 10114 ki te 2033, ka 12147.

$$12147+2039=13x^{2}$$

Tāpirihia te 12147 ki te 2039, ka 14186.

$$14186=13x^{2}$$

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

$$13x^{2}=14186$$

Whakawehea ngā taha e rua ki te 13.

$$x^{2}=\frac{14186}{13}$$

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

$$x=\frac{\sqrt{184418}}{13} x=-\frac{\sqrt{184418}}{13}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 13.

$$2020+2022+2023+2024+2025+2033+2039=13xx$$

Whakareatia te x ki te x, ka x^{2}.

$$2020+2022+2023+2024+2025+2033+2039=13x^{2}$$

Tāpirihia te 2020 ki te 2022, ka 4042.

$$4042+2023+2024+2025+2033+2039=13x^{2}$$

Tāpirihia te 4042 ki te 2023, ka 6065.

$$6065+2024+2025+2033+2039=13x^{2}$$

Tāpirihia te 6065 ki te 2024, ka 8089.

$$8089+2025+2033+2039=13x^{2}$$

Tāpirihia te 8089 ki te 2025, ka 10114.

$$10114+2033+2039=13x^{2}$$

Tāpirihia te 10114 ki te 2033, ka 12147.

$$12147+2039=13x^{2}$$

Tāpirihia te 12147 ki te 2039, ka 14186.

$$14186=13x^{2}$$

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

$$13x^{2}=14186$$

Tangohia te 14186 mai i ngā taha e rua.

$$13x^{2}-14186=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 13 mō a, 0 mō b, me -14186 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-14186\right)}}{2\times 13}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-14186\right)}}{2\times 13}$$

Whakareatia -4 ki te 13.

$$x=\frac{0±\sqrt{-52\left(-14186\right)}}{2\times 13}$$

Whakareatia -52 ki te -14186.

$$x=\frac{0±\sqrt{737672}}{2\times 13}$$

Tuhia te pūtakerua o te 737672.

$$x=\frac{0±2\sqrt{184418}}{2\times 13}$$

Whakareatia 2 ki te 13.

$$x=\frac{0±2\sqrt{184418}}{26}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{184418}}{26} ina he tāpiri te ±.

$$x=\frac{\sqrt{184418}}{13}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{184418}}{26} ina he tango te ±.

$$x=-\frac{\sqrt{184418}}{13}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{184418}}{13} x=-\frac{\sqrt{184418}}{13}$$