Whakaoti i te f(x)=-x^2+2ax+1=a

$$f ( x ) = - x ^ { 2 } + 2 a x + 1 = a$$

Whakaoti mō a

$$a=-\frac{1-x^{2}}{2x-1}$$

$$x\neq \frac{1}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te a mai i ngā taha e rua.

$$-x^{2}+2ax+1-a=0$$

Me tāpiri te x^{2} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2ax+1-a=x^{2}$$

Tangohia te 1 mai i ngā taha e rua.

$$2ax-a=x^{2}-1$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

$$\left(2x-1\right)a=x^{2}-1$$

Whakawehea ngā taha e rua ki te 2x-1.

$$\frac{\left(2x-1\right)a}{2x-1}=\frac{x^{2}-1}{2x-1}$$

Mā te whakawehe ki te 2x-1 ka wetekia te whakareanga ki te 2x-1.

$$a=\frac{x^{2}-1}{2x-1}$$

Whakaoti mō x

$$x=-\sqrt{a^{2}-a+1}+a$$

$$x=\sqrt{a^{2}-a+1}+a$$