Whakaoti i te 3^2+(4-2t)^2=(2t)^2

$$3 ^ { 2 } + ( 4 - 2 t ) ^ { 2 } = ( 2 t ) ^ { 2 }$$

Whakaoti mō t

$$t = \frac{25}{16} = 1\frac{9}{16} = 1.5625$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$9+\left(4-2t\right)^{2}=\left(2t\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(4-2t\right)^{2}.

$$9+16-16t+4t^{2}=\left(2t\right)^{2}$$

Tāpirihia te 9 ki te 16, ka 25.

$$25-16t+4t^{2}=\left(2t\right)^{2}$$

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

$$25-16t+4t^{2}=2^{2}t^{2}$$

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

$$25-16t+4t^{2}=4t^{2}$$

Tangohia te 4t^{2} mai i ngā taha e rua.

$$25-16t+4t^{2}-4t^{2}=0$$

Pahekotia te 4t^{2} me -4t^{2}, ka 0.

$$25-16t=0$$

Tangohia te 25 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-16t=-25$$

Whakawehea ngā taha e rua ki te -16.

$$t=\frac{-25}{-16}$$

Ka taea te hautanga \frac{-25}{-16} te whakamāmā ki te \frac{25}{16} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$t=\frac{25}{16}$$