Whakaoti i te 25x=sqrt{49x^2+48^2}

$$25x= \sqrt{ 49 { x }^{ 2 } + { 48 }^{ 2 } }$$

Whakaoti mō x

$$x=2$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(25x\right)^{2}=\left(\sqrt{49x^{2}+48^{2}}\right)^{2}$$

Whakarohaina te \left(25x\right)^{2}.

$$25^{2}x^{2}=\left(\sqrt{49x^{2}+48^{2}}\right)^{2}$$

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$625x^{2}=\left(\sqrt{49x^{2}+48^{2}}\right)^{2}$$

Tātaihia te 48 mā te pū o 2, kia riro ko 2304.

$$625x^{2}=\left(\sqrt{49x^{2}+2304}\right)^{2}$$

Tātaihia te \sqrt{49x^{2}+2304} mā te pū o 2, kia riro ko 49x^{2}+2304.

$$625x^{2}=49x^{2}+2304$$

Tangohia te 49x^{2} mai i ngā taha e rua.

$$625x^{2}-49x^{2}=2304$$

Pahekotia te 625x^{2} me -49x^{2}, ka 576x^{2}.

$$576x^{2}=2304$$

Tangohia te 2304 mai i ngā taha e rua.

$$576x^{2}-2304=0$$

Whakawehea ngā taha e rua ki te 576.

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

Whakaarohia te x^{2}-4. Tuhia anō te x^{2}-4 hei x^{2}-2^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te x+2=0.

$$x=2 x=-2$$

Whakakapia te 2 mō te x i te whārite 25x=\sqrt{49x^{2}+48^{2}}.

$$25\times 2=\sqrt{49\times 2^{2}+48^{2}}$$

Whakarūnātia. Ko te uara x=2 kua ngata te whārite.

$$50=50$$

Whakakapia te -2 mō te x i te whārite 25x=\sqrt{49x^{2}+48^{2}}.

$$25\left(-2\right)=\sqrt{49\left(-2\right)^{2}+48^{2}}$$

Whakarūnātia. Ko te uara x=-2 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-50=50$$

Ko te whārite 25x=\sqrt{49x^{2}+2304} he rongoā ahurei.

$$x=2$$