Whakaoti i te (4x)^2+(3x)^2=37^2

$$( 4 x ) ^ { 2 } + ( 3 x ) ^ { 2 } = 37 ^ { 2 }$$

Whakaoti mō x

$$x = -\frac{37}{5} = -7\frac{2}{5} = -7.4$$

$$x = \frac{37}{5} = 7\frac{2}{5} = 7.4$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}+\left(3x\right)^{2}=37^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}+\left(3x\right)^{2}=37^{2}$$

Whakarohaina te \left(3x\right)^{2}.

$$16x^{2}+3^{2}x^{2}=37^{2}$$

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

$$16x^{2}+9x^{2}=37^{2}$$

Pahekotia te 16x^{2} me 9x^{2}, ka 25x^{2}.

$$25x^{2}=37^{2}$$

Tātaihia te 37 mā te pū o 2, kia riro ko 1369.

$$25x^{2}=1369$$

Tangohia te 1369 mai i ngā taha e rua.

$$25x^{2}-1369=0$$

Whakaarohia te 25x^{2}-1369. Tuhia anō te 25x^{2}-1369 hei \left(5x\right)^{2}-37^{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).

$$\left(5x-37\right)\left(5x+37\right)=0$$

Hei kimi otinga whārite, me whakaoti te 5x-37=0 me te 5x+37=0.

$$x=\frac{37}{5} x=-\frac{37}{5}$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}+\left(3x\right)^{2}=37^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}+\left(3x\right)^{2}=37^{2}$$

Whakarohaina te \left(3x\right)^{2}.

$$16x^{2}+3^{2}x^{2}=37^{2}$$

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

$$16x^{2}+9x^{2}=37^{2}$$

Pahekotia te 16x^{2} me 9x^{2}, ka 25x^{2}.

$$25x^{2}=37^{2}$$

Tātaihia te 37 mā te pū o 2, kia riro ko 1369.

$$25x^{2}=1369$$

Whakawehea ngā taha e rua ki te 25.

$$x^{2}=\frac{1369}{25}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$x=\frac{37}{5} x=-\frac{37}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}+\left(3x\right)^{2}=37^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}+\left(3x\right)^{2}=37^{2}$$

Whakarohaina te \left(3x\right)^{2}.

$$16x^{2}+3^{2}x^{2}=37^{2}$$

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

$$16x^{2}+9x^{2}=37^{2}$$

Pahekotia te 16x^{2} me 9x^{2}, ka 25x^{2}.

$$25x^{2}=37^{2}$$

Tātaihia te 37 mā te pū o 2, kia riro ko 1369.

$$25x^{2}=1369$$

Tangohia te 1369 mai i ngā taha e rua.

$$25x^{2}-1369=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, 0 mō b, me -1369 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-1369\right)}}{2\times 25}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-1369\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$x=\frac{0±\sqrt{-100\left(-1369\right)}}{2\times 25}$$

Whakareatia -100 ki te -1369.

$$x=\frac{0±\sqrt{136900}}{2\times 25}$$

Tuhia te pūtakerua o te 136900.

$$x=\frac{0±370}{2\times 25}$$

Whakareatia 2 ki te 25.

$$x=\frac{0±370}{50}$$

Nā, me whakaoti te whārite x=\frac{0±370}{50} ina he tāpiri te ±. Whakahekea te hautanga \frac{370}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x=\frac{37}{5}$$

Nā, me whakaoti te whārite x=\frac{0±370}{50} ina he tango te ±. Whakahekea te hautanga \frac{-370}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x=-\frac{37}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{37}{5} x=-\frac{37}{5}$$