Whakaoti i te (3+x)^2=(3-x)^2+16

$$( 3 + x ) ^ { 2 } = ( 3 - x ) ^ { 2 } + 16$$

Whakaoti mō x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(3+x\right)^{2}.

$$9+6x+x^{2}=\left(3-x\right)^{2}+16$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(3-x\right)^{2}.

$$9+6x+x^{2}=9-6x+x^{2}+16$$

Tāpirihia te 9 ki te 16, ka 25.

$$9+6x+x^{2}=25-6x+x^{2}$$

Me tāpiri te 6x ki ngā taha e rua.

$$9+6x+x^{2}+6x=25+x^{2}$$

Pahekotia te 6x me 6x, ka 12x.

$$9+12x+x^{2}=25+x^{2}$$

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

$$9+12x+x^{2}-x^{2}=25$$

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

$$9+12x=25$$

Tangohia te 9 mai i ngā taha e rua.

$$12x=25-9$$

Tangohia te 9 i te 25, ka 16.

$$12x=16$$

Whakawehea ngā taha e rua ki te 12.

$$x=\frac{16}{12}$$

Whakahekea te hautanga \frac{16}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{4}{3}$$