Whakaoti i te 9a-20=sqrt{400-a^2}

$$9 a - 20 = \sqrt { 400 - a ^ { 2 } }$$

Whakaoti mō a

$$a = \frac{180}{41} = 4\frac{16}{41} \approx 4.390243902$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(9a-20\right)^{2}=\left(\sqrt{400-a^{2}}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(9a-20\right)^{2}.

$$81a^{2}-360a+400=\left(\sqrt{400-a^{2}}\right)^{2}$$

Tātaihia te \sqrt{400-a^{2}} mā te pū o 2, kia riro ko 400-a^{2}.

$$81a^{2}-360a+400=400-a^{2}$$

Tangohia te 400 mai i ngā taha e rua.

$$81a^{2}-360a+400-400=-a^{2}$$

Tangohia te 400 i te 400, ka 0.

$$81a^{2}-360a=-a^{2}$$

Me tāpiri te a^{2} ki ngā taha e rua.

$$81a^{2}-360a+a^{2}=0$$

Pahekotia te 81a^{2} me a^{2}, ka 82a^{2}.

$$82a^{2}-360a=0$$

Tauwehea te a.

$$a\left(82a-360\right)=0$$

Hei kimi otinga whārite, me whakaoti te a=0 me te 82a-360=0.

$$a=0 a=\frac{180}{41}$$

Whakakapia te 0 mō te a i te whārite 9a-20=\sqrt{400-a^{2}}.

$$9\times 0-20=\sqrt{400-0^{2}}$$

Whakarūnātia. Ko te uara a=0 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-20=20$$

Whakakapia te \frac{180}{41} mō te a i te whārite 9a-20=\sqrt{400-a^{2}}.

$$9\times \frac{180}{41}-20=\sqrt{400-\left(\frac{180}{41}\right)^{2}}$$

Whakarūnātia. Ko te uara a=\frac{180}{41} kua ngata te whārite.

$$\frac{800}{41}=\frac{800}{41}$$

Ko te whārite 9a-20=\sqrt{400-a^{2}} he rongoā ahurei.

$$a=\frac{180}{41}$$