Whakaoti i te (a-x)^2+3^2=x^2

$$( a - x ) ^ { 2 } + 3 ^ { 2 } = x ^ { 2 }$$

Whakaoti mō x

$$x=\frac{a}{2}+\frac{9}{2a}$$

$$a\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(a-x\right)^{2}.

$$a^{2}-2ax+x^{2}+3^{2}=x^{2}$$

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

$$a^{2}-2ax+x^{2}+9=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$a^{2}-2ax+x^{2}+9-x^{2}=0$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$a^{2}-2ax+9=0$$

Tangohia te a^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-2ax+9=-a^{2}$$

Tangohia te 9 mai i ngā taha e rua.

$$-2ax=-a^{2}-9$$

He hanga arowhānui tō te whārite.

$$\left(-2a\right)x=-a^{2}-9$$

Whakawehea ngā taha e rua ki te -2a.

$$\frac{\left(-2a\right)x}{-2a}=\frac{-a^{2}-9}{-2a}$$

Mā te whakawehe ki te -2a ka wetekia te whakareanga ki te -2a.

$$x=\frac{-a^{2}-9}{-2a}$$

Whakawehe -a^{2}-9 ki te -2a.

$$x=\frac{a}{2}+\frac{9}{2a}$$

Whakaoti mō a (complex solution)

$$a=-\sqrt{x^{2}-9}+x$$

$$a=\sqrt{x^{2}-9}+x$$

Whakaoti mō a

$$a=-\sqrt{x^{2}-9}+x$$

$$a=\sqrt{x^{2}-9}+x\text{, }|x|\geq 3$$