Whakaoti i te 5x+3=sqrt{3x+7}

$$5 x + 3 = \sqrt { 3 x + 7 }$$

Whakaoti mō x

$$x=-\frac{2}{25}=-0.08$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(5x+3\right)^{2}=\left(\sqrt{3x+7}\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(5x+3\right)^{2}.

$$25x^{2}+30x+9=\left(\sqrt{3x+7}\right)^{2}$$

Tātaihia te \sqrt{3x+7} mā te pū o 2, kia riro ko 3x+7.

$$25x^{2}+30x+9=3x+7$$

Tangohia te 3x mai i ngā taha e rua.

$$25x^{2}+30x+9-3x=7$$

Pahekotia te 30x me -3x, ka 27x.

$$25x^{2}+27x+9=7$$

Tangohia te 7 mai i ngā taha e rua.

$$25x^{2}+27x+9-7=0$$

Tangohia te 7 i te 9, ka 2.

$$25x^{2}+27x+2=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 25x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=27 ab=25\times 2=50$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 50.

$$1,50 2,25 5,10$$

Tātaihia te tapeke mō ia takirua.

$$1+50=51 2+25=27 5+10=15$$

Ko te otinga te takirua ka hoatu i te tapeke 27.

$$a=2 b=25$$

Tuhia anō te 25x^{2}+27x+2 hei \left(25x^{2}+2x\right)+\left(25x+2\right).

$$\left(25x^{2}+2x\right)+\left(25x+2\right)$$

Whakatauwehea atu x i te 25x^{2}+2x.

$$x\left(25x+2\right)+25x+2$$

Whakatauwehea atu te kīanga pātahi 25x+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(25x+2\right)\left(x+1\right)$$

Hei kimi otinga whārite, me whakaoti te 25x+2=0 me te x+1=0.

$$x=-\frac{2}{25} x=-1$$

Whakakapia te -\frac{2}{25} mō te x i te whārite 5x+3=\sqrt{3x+7}.

$$5\left(-\frac{2}{25}\right)+3=\sqrt{3\left(-\frac{2}{25}\right)+7}$$

Whakarūnātia. Ko te uara x=-\frac{2}{25} kua ngata te whārite.

$$\frac{13}{5}=\frac{13}{5}$$

Whakakapia te -1 mō te x i te whārite 5x+3=\sqrt{3x+7}.

$$5\left(-1\right)+3=\sqrt{3\left(-1\right)+7}$$

Whakarūnātia. Ko te uara x=-1 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-2=2$$

Ko te whārite 5x+3=\sqrt{3x+7} he rongoā ahurei.

$$x=-\frac{2}{25}$$