Whakaoti i te 4(x^2-49)+61geq(2x-5)^2

$$4 ( x ^ { 2 } - 49 ) + 61 \geq ( 2 x - 5 ) ^ { 2 }$$

Whakaoti mō x

$$x\geq 8$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}-49.

$$4x^{2}-196+61\geq \left(2x-5\right)^{2}$$

Tāpirihia te -196 ki te 61, ka -135.

$$4x^{2}-135\geq \left(2x-5\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$4x^{2}-135\geq 4x^{2}-20x+25$$

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

$$4x^{2}-135-4x^{2}\geq -20x+25$$

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

$$-135\geq -20x+25$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa. Ka huri tēnei i te aronga o te tohu.

$$-20x+25\leq -135$$

Tangohia te 25 mai i ngā taha e rua.

$$-20x\leq -135-25$$

Tangohia te 25 i te -135, ka -160.

$$-20x\leq -160$$

Whakawehea ngā taha e rua ki te -20. I te mea he tōraro a -20, ka huri te ahunga koreōrite.

$$x\geq \frac{-160}{-20}$$

Whakawehea te -160 ki te -20, kia riro ko 8.

$$x\geq 8$$