Whakaoti i te 7.5^2+x^2=8.5^2

$$7.5 ^ { 2 } + x ^ { 2 } = 8.5 ^ { 2 }$$

Whakaoti mō x

$$x=-4$$

$$x=4$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tātaihia te 7.5 mā te pū o 2, kia riro ko 56.25.

$$56.25+x^{2}=8.5^{2}$$

Tātaihia te 8.5 mā te pū o 2, kia riro ko 72.25.

$$56.25+x^{2}=72.25$$

Tangohia te 72.25 mai i ngā taha e rua.

$$56.25+x^{2}-72.25=0$$

Tangohia te 72.25 i te 56.25, ka -16.

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

Whakaarohia te -16+x^{2}. Tuhia anō te -16+x^{2} hei x^{2}-4^{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).

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

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

$$x=4 x=-4$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 7.5 mā te pū o 2, kia riro ko 56.25.

$$56.25+x^{2}=8.5^{2}$$

Tātaihia te 8.5 mā te pū o 2, kia riro ko 72.25.

$$56.25+x^{2}=72.25$$

Tangohia te 56.25 mai i ngā taha e rua.

$$x^{2}=72.25-56.25$$

Tangohia te 56.25 i te 72.25, ka 16.

$$x^{2}=16$$

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

$$x=4 x=-4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 7.5 mā te pū o 2, kia riro ko 56.25.

$$56.25+x^{2}=8.5^{2}$$

Tātaihia te 8.5 mā te pū o 2, kia riro ko 72.25.

$$56.25+x^{2}=72.25$$

Tangohia te 72.25 mai i ngā taha e rua.

$$56.25+x^{2}-72.25=0$$

Tangohia te 72.25 i te 56.25, ka -16.

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

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Whakareatia -4 ki te -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{0±8}{2}$$

Nā, me whakaoti te whārite x=\frac{0±8}{2} ina he tāpiri te ±. Whakawehe 8 ki te 2.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{0±8}{2} ina he tango te ±. Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=4 x=-4$$