Whakaoti i te sqrt{15x^2}=sqrt{4-left(2-xright)^2}

$$\sqrt{ 15 { x }^{ 2 } } = \sqrt{ 4- { \left(2-x \right) }^{ 2 } }$$

Whakaoti mō x

$$x=\frac{1}{4}=0.25$$

$$x=0$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{15x^{2}}\right)^{2}=\left(\sqrt{4-\left(2-x\right)^{2}}\right)^{2}$$

Tātaihia te \sqrt{15x^{2}} mā te pū o 2, kia riro ko 15x^{2}.

$$15x^{2}=\left(\sqrt{4-\left(2-x\right)^{2}}\right)^{2}$$

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

$$15x^{2}=\left(\sqrt{4-\left(4-4x+x^{2}\right)}\right)^{2}$$

Hei kimi i te tauaro o 4-4x+x^{2}, kimihia te tauaro o ia taurangi.

$$15x^{2}=\left(\sqrt{4-4+4x-x^{2}}\right)^{2}$$

Tangohia te 4 i te 4, ka 0.

$$15x^{2}=\left(\sqrt{4x-x^{2}}\right)^{2}$$

Tātaihia te \sqrt{4x-x^{2}} mā te pū o 2, kia riro ko 4x-x^{2}.

$$15x^{2}=4x-x^{2}$$

Tangohia te 4x mai i ngā taha e rua.

$$15x^{2}-4x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$15x^{2}-4x+x^{2}=0$$

Pahekotia te 15x^{2} me x^{2}, ka 16x^{2}.

$$16x^{2}-4x=0$$

Tauwehea te x.

$$x\left(16x-4\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 16x-4=0.

$$x=0 x=\frac{1}{4}$$

Whakakapia te 0 mō te x i te whārite \sqrt{15x^{2}}=\sqrt{4-\left(2-x\right)^{2}}.

$$\sqrt{15\times 0^{2}}=\sqrt{4-\left(2-0\right)^{2}}$$

Whakarūnātia. Ko te uara x=0 kua ngata te whārite.

$$0=0$$

Whakakapia te \frac{1}{4} mō te x i te whārite \sqrt{15x^{2}}=\sqrt{4-\left(2-x\right)^{2}}.

$$\sqrt{15\times \left(\frac{1}{4}\right)^{2}}=\sqrt{4-\left(2-\frac{1}{4}\right)^{2}}$$

Whakarūnātia. Ko te uara x=\frac{1}{4} kua ngata te whārite.

$$\frac{1}{4}\times 15^{\frac{1}{2}}=\frac{1}{4}\times 15^{\frac{1}{2}}$$

Rārangihia ngā rongoā katoa o \sqrt{15x^{2}}=\sqrt{4-\left(2-x\right)^{2}}.

$$x=0 x=\frac{1}{4}$$