Whakaoti i te sqrt{x}+sqrt{x+7}=17

$$\sqrt { x } + \sqrt { x + 7 } = 17$$

Whakaoti mō x

$$x = \frac{19881}{289} = 68\frac{229}{289} \approx 68.792387543$$

Ngā Upane Otinga

Me tango \sqrt{x+7} mai i ngā taha e rua o te whārite.

$$\sqrt{x}=17-\sqrt{x+7}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x}\right)^{2}=\left(17-\sqrt{x+7}\right)^{2}$$

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

$$x=\left(17-\sqrt{x+7}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(17-\sqrt{x+7}\right)^{2}.

$$x=289-34\sqrt{x+7}+\left(\sqrt{x+7}\right)^{2}$$

Tātaihia te \sqrt{x+7} mā te pū o 2, kia riro ko x+7.

$$x=289-34\sqrt{x+7}+x+7$$

Tāpirihia te 289 ki te 7, ka 296.

$$x=296-34\sqrt{x+7}+x$$

Me tāpiri te 34\sqrt{x+7} ki ngā taha e rua.

$$x+34\sqrt{x+7}=296+x$$

Tangohia te x mai i ngā taha e rua.

$$x+34\sqrt{x+7}-x=296$$

Pahekotia te x me -x, ka 0.

$$34\sqrt{x+7}=296$$

Whakawehea ngā taha e rua ki te 34.

$$\sqrt{x+7}=\frac{296}{34}$$

Whakahekea te hautanga \frac{296}{34} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{x+7}=\frac{148}{17}$$

Pūruatia ngā taha e rua o te whārite.

$$x+7=\frac{21904}{289}$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$x+7-7=\frac{21904}{289}-7$$

Mā te tango i te 7 i a ia ake anō ka toe ko te 0.

$$x=\frac{21904}{289}-7$$

Tango 7 mai i \frac{21904}{289}.

$$x=\frac{19881}{289}$$

Whakakapia te \frac{19881}{289} mō te x i te whārite \sqrt{x}+\sqrt{x+7}=17.

$$\sqrt{\frac{19881}{289}}+\sqrt{\frac{19881}{289}+7}=17$$

Whakarūnātia. Ko te uara x=\frac{19881}{289} kua ngata te whārite.

$$17=17$$

Ko te whārite \sqrt{x}=-\sqrt{x+7}+17 he rongoā ahurei.

$$x=\frac{19881}{289}$$