Whakaoti i te {left(x/3right)}^2-15=7

$${ \left( \frac{ x }{ 3 } \right) }^{ 2 } -15=7$$

Whakaoti mō x

$$x=3\sqrt{22}\approx 14.071247279$$

$$x=-3\sqrt{22}\approx -14.071247279$$

Ngā Upane mā te Kimi Pūtakerua

Kia whakarewa i te \frac{x}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{x^{2}}{3^{2}}-15=7$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 15 ki te \frac{3^{2}}{3^{2}}.

$$\frac{x^{2}}{3^{2}}-\frac{15\times 3^{2}}{3^{2}}=7$$

Tā te mea he rite te tauraro o \frac{x^{2}}{3^{2}} me \frac{15\times 3^{2}}{3^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x^{2}-15\times 3^{2}}{3^{2}}=7$$

Mahia ngā whakarea i roto o x^{2}-15\times 3^{2}.

$$\frac{x^{2}-135}{3^{2}}=7$$

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

$$\frac{x^{2}-135}{9}=7$$

Whakawehea ia wā o x^{2}-135 ki te 9, kia riro ko \frac{1}{9}x^{2}-15.

$$\frac{1}{9}x^{2}-15=7$$

Me tāpiri te 15 ki ngā taha e rua.

$$\frac{1}{9}x^{2}=7+15$$

Tāpirihia te 7 ki te 15, ka 22.

$$\frac{1}{9}x^{2}=22$$

Me whakarea ngā taha e rua ki te 9, te tau utu o \frac{1}{9}.

$$x^{2}=22\times 9$$

Whakareatia te 22 ki te 9, ka 198.

$$x^{2}=198$$

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

$$x=3\sqrt{22} x=-3\sqrt{22}$$