Whakaoti i te 3^2+6^2+9^2+12^2+{15}^{2}+{18}^{2}+{21}^2+{24}^2+{27}^2+{30}^2=x

$${ 3 }^{ 2 } + { 6 }^{ 2 } + { 9 }^{ 2 } + { 12 }^{ 2 } + { 15 }^{ 2 } + { 18 }^{ 2 } + { 21 }^{ 2 } + { 24 }^{ 2 } + { 27 }^{ 2 } + { 30 }^{ 2 } =x$$

Whakaoti mō x

$$x=3465$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9+6^{2}+9^{2}+12^{2}+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$9+36+9^{2}+12^{2}+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tāpirihia te 9 ki te 36, ka 45.

$$45+9^{2}+12^{2}+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$45+81+12^{2}+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tāpirihia te 45 ki te 81, ka 126.

$$126+12^{2}+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 12 mā te pū o 2, kia riro ko 144.

$$126+144+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tāpirihia te 126 ki te 144, ka 270.

$$270+15^{2}+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 15 mā te pū o 2, kia riro ko 225.

$$270+225+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tāpirihia te 270 ki te 225, ka 495.

$$495+18^{2}+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 18 mā te pū o 2, kia riro ko 324.

$$495+324+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tāpirihia te 495 ki te 324, ka 819.

$$819+21^{2}+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 21 mā te pū o 2, kia riro ko 441.

$$819+441+24^{2}+27^{2}+30^{2}=x$$

Tāpirihia te 819 ki te 441, ka 1260.

$$1260+24^{2}+27^{2}+30^{2}=x$$

Tātaihia te 24 mā te pū o 2, kia riro ko 576.

$$1260+576+27^{2}+30^{2}=x$$

Tāpirihia te 1260 ki te 576, ka 1836.

$$1836+27^{2}+30^{2}=x$$

Tātaihia te 27 mā te pū o 2, kia riro ko 729.

$$1836+729+30^{2}=x$$

Tāpirihia te 1836 ki te 729, ka 2565.

$$2565+30^{2}=x$$

Tātaihia te 30 mā te pū o 2, kia riro ko 900.

$$2565+900=x$$

Tāpirihia te 2565 ki te 900, ka 3465.

$$3465=x$$

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

$$x=3465$$