Whakaoti i te 20/(1+x)^2=19/x^2

$$\frac { 20 } { ( 1 + x ) ^ { 2 } } = \frac { 19 } { x ^ { 2 } }$$

Whakaoti mō x

$$x=2\sqrt{95}+19\approx 38.49358869$$

$$x=19-2\sqrt{95}\approx -0.49358869$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x^{2}\left(x+1\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o \left(1+x\right)^{2},x^{2}.

$$x^{2}\times 20=\left(x+1\right)^{2}\times 19$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$x^{2}\times 20=\left(x^{2}+2x+1\right)\times 19$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+2x+1 ki te 19.

$$x^{2}\times 20=19x^{2}+38x+19$$

Tangohia te 19x^{2} mai i ngā taha e rua.

$$x^{2}\times 20-19x^{2}=38x+19$$

Pahekotia te x^{2}\times 20 me -19x^{2}, ka x^{2}.

$$x^{2}=38x+19$$

Tangohia te 38x mai i ngā taha e rua.

$$x^{2}-38x=19$$

Tangohia te 19 mai i ngā taha e rua.

$$x^{2}-38x-19=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -38 mō b, me -19 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-38\right)±\sqrt{\left(-38\right)^{2}-4\left(-19\right)}}{2}$$

Pūrua -38.

$$x=\frac{-\left(-38\right)±\sqrt{1444-4\left(-19\right)}}{2}$$

Whakareatia -4 ki te -19.

$$x=\frac{-\left(-38\right)±\sqrt{1444+76}}{2}$$

Tāpiri 1444 ki te 76.

$$x=\frac{-\left(-38\right)±\sqrt{1520}}{2}$$

Tuhia te pūtakerua o te 1520.

$$x=\frac{-\left(-38\right)±4\sqrt{95}}{2}$$

Ko te tauaro o -38 ko 38.

$$x=\frac{38±4\sqrt{95}}{2}$$

Nā, me whakaoti te whārite x=\frac{38±4\sqrt{95}}{2} ina he tāpiri te ±. Tāpiri 38 ki te 4\sqrt{95}.

$$x=\frac{4\sqrt{95}+38}{2}$$

Whakawehe 38+4\sqrt{95} ki te 2.

$$x=2\sqrt{95}+19$$

Nā, me whakaoti te whārite x=\frac{38±4\sqrt{95}}{2} ina he tango te ±. Tango 4\sqrt{95} mai i 38.

$$x=\frac{38-4\sqrt{95}}{2}$$

Whakawehe 38-4\sqrt{95} ki te 2.

$$x=19-2\sqrt{95}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{95}+19 x=19-2\sqrt{95}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x^{2}\left(x+1\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o \left(1+x\right)^{2},x^{2}.

$$x^{2}\times 20=\left(x+1\right)^{2}\times 19$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$x^{2}\times 20=\left(x^{2}+2x+1\right)\times 19$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+2x+1 ki te 19.

$$x^{2}\times 20=19x^{2}+38x+19$$

Tangohia te 19x^{2} mai i ngā taha e rua.

$$x^{2}\times 20-19x^{2}=38x+19$$

Pahekotia te x^{2}\times 20 me -19x^{2}, ka x^{2}.

$$x^{2}=38x+19$$

Tangohia te 38x mai i ngā taha e rua.

$$x^{2}-38x=19$$

Whakawehea te -38, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -19. Nā, tāpiria te pūrua o te -19 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-38x+\left(-19\right)^{2}=19+\left(-19\right)^{2}$$

Pūrua -19.

$$x^{2}-38x+361=19+361$$

Tāpiri 19 ki te 361.

$$x^{2}-38x+361=380$$

Tauwehea x^{2}-38x+361. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-19\right)^{2}=380$$

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

$$\sqrt{\left(x-19\right)^{2}}=\sqrt{380}$$

Whakarūnātia.

$$x-19=2\sqrt{95} x-19=-2\sqrt{95}$$

Me tāpiri 19 ki ngā taha e rua o te whārite.

$$x=2\sqrt{95}+19 x=19-2\sqrt{95}$$