Whakaoti i te sqrt{x+3}+sqrt{x-3}=6

$$\sqrt { x + 3 } + \sqrt { x - 3 } = 6$$

Whakaoti mō x

$$x = \frac{37}{4} = 9\frac{1}{4} = 9.25$$

Ngā Upane Otinga

Me tango \sqrt{x-3} mai i ngā taha e rua o te whārite.

$$\sqrt{x+3}=6-\sqrt{x-3}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x+3}\right)^{2}=\left(6-\sqrt{x-3}\right)^{2}$$

Tātaihia te \sqrt{x+3} mā te pū o 2, kia riro ko x+3.

$$x+3=\left(6-\sqrt{x-3}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(6-\sqrt{x-3}\right)^{2}.

$$x+3=36-12\sqrt{x-3}+\left(\sqrt{x-3}\right)^{2}$$

Tātaihia te \sqrt{x-3} mā te pū o 2, kia riro ko x-3.

$$x+3=36-12\sqrt{x-3}+x-3$$

Tangohia te 3 i te 36, ka 33.

$$x+3=33-12\sqrt{x-3}+x$$

Me tāpiri te 12\sqrt{x-3} ki ngā taha e rua.

$$x+3+12\sqrt{x-3}=33+x$$

Tangohia te x mai i ngā taha e rua.

$$x+3+12\sqrt{x-3}-x=33$$

Pahekotia te x me -x, ka 0.

$$3+12\sqrt{x-3}=33$$

Tangohia te 3 mai i ngā taha e rua.

$$12\sqrt{x-3}=33-3$$

Tangohia te 3 i te 33, ka 30.

$$12\sqrt{x-3}=30$$

Whakawehea ngā taha e rua ki te 12.

$$\sqrt{x-3}=\frac{30}{12}$$

Whakahekea te hautanga \frac{30}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\sqrt{x-3}=\frac{5}{2}$$

Pūruatia ngā taha e rua o te whārite.

$$x-3=\frac{25}{4}$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x-3-\left(-3\right)=\frac{25}{4}-\left(-3\right)$$

Mā te tango i te -3 i a ia ake anō ka toe ko te 0.

$$x=\frac{25}{4}-\left(-3\right)$$

Tango -3 mai i \frac{25}{4}.

$$x=\frac{37}{4}$$

Whakakapia te \frac{37}{4} mō te x i te whārite \sqrt{x+3}+\sqrt{x-3}=6.

$$\sqrt{\frac{37}{4}+3}+\sqrt{\frac{37}{4}-3}=6$$

Whakarūnātia. Ko te uara x=\frac{37}{4} kua ngata te whārite.

$$6=6$$

Ko te whārite \sqrt{x+3}=-\sqrt{x-3}+6 he rongoā ahurei.

$$x=\frac{37}{4}$$