x(2+16+24m^2-9m^4/2(3m^2+4))*2/m=frac{sqrt{6}}{2}*2 eching

$$x ( 2 + \frac { 16 + 24 m ^ { 2 } - 9 m ^ { 4 } } { 2 ( 3 m ^ { 2 } + 4 ) } ) \times \frac { 2 } { m } = \frac { \sqrt { 6 } } { 2 } \times 2$$

x uchun yechish

$$x=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}$$

$$m\neq 0\text{ and }|m|\neq \frac{\sqrt{6\sqrt{17}+18}}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2m\left(3m^{2}+4\right) ga, 2\left(3m^{2}+4\right),m,2 ning eng kichik karralisiga ko‘paytiring.

$$x\left(2+\frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\right)\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)} marotabaga ko'paytirish.

$$x\left(\frac{2\times 2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)}+\frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\right)\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

\frac{2\times 2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)} va \frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$x\times \frac{2\times 2\left(3m^{2}+4\right)+16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

2\times 2\left(3m^{2}+4\right)+16+24m^{2}-9m^{4} ichidagi ko‘paytirishlarni bajaring.

$$x\times \frac{12m^{2}+16+16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

12m^{2}+16+16+24m^{2}-9m^{4} kabi iboralarga o‘xshab birlashtiring.

$$x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)} ni yagona kasrga aylantiring.

$$\frac{x\left(36m^{2}+32-9m^{4}\right)}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

\frac{x\left(36m^{2}+32-9m^{4}\right)}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right) ni yagona kasrga aylantiring.

$$\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}\times 2=2m\left(3m^{2}+4\right)\sqrt{6}$$

\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}\times 2 ni yagona kasrga aylantiring.

$$\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)\times 2}{2\left(3m^{2}+4\right)}=2m\left(3m^{2}+4\right)\sqrt{6}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}=2m\left(3m^{2}+4\right)\sqrt{6}$$

2m ga 3m^{2}+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}=\left(6m^{3}+8m\right)\sqrt{6}$$

6m^{3}+8m ga \sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4}=6m^{3}\sqrt{6}+8m\sqrt{6}$$

\frac{x\left(6m^{2}+8\right)\left(-9m^{4}+36m^{2}+32\right)}{3m^{2}+4} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{-2\times 9x\left(3m^{2}+4\right)\left(m^{2}-\left(-\frac{2}{3}\sqrt{17}+2\right)\right)\left(m^{2}-\left(\frac{2}{3}\sqrt{17}+2\right)\right)}{3m^{2}+4}=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Surat va maxrajdagi ikkala 3m^{2}+4 ni qisqartiring.

$$-2\times 9x\left(m^{2}-\left(-\frac{2}{3}\sqrt{17}+2\right)\right)\left(m^{2}-\left(\frac{2}{3}\sqrt{17}+2\right)\right)=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Ifodani kengaytiring.

$$-18xm^{4}+72xm^{2}+64x=6m^{3}\sqrt{6}+8m\sqrt{6}$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-18m^{4}+72m^{2}+64\right)x=6m^{3}\sqrt{6}+8m\sqrt{6}$$

Tenglama standart shaklda.

$$\left(64+72m^{2}-18m^{4}\right)x=6\sqrt{6}m^{3}+8\sqrt{6}m$$

Ikki tarafini -18m^{4}+72m^{2}+64 ga bo‘ling.

$$\frac{\left(64+72m^{2}-18m^{4}\right)x}{64+72m^{2}-18m^{4}}=\frac{2\sqrt{6}m\left(3m^{2}+4\right)}{64+72m^{2}-18m^{4}}$$

-18m^{4}+72m^{2}+64 ga bo'lish -18m^{4}+72m^{2}+64 ga ko'paytirishni bekor qiladi.

$$x=\frac{2\sqrt{6}m\left(3m^{2}+4\right)}{64+72m^{2}-18m^{4}}$$

2m\left(3m^{2}+4\right)\sqrt{6} ni -18m^{4}+72m^{2}+64 ga bo'lish.

$$x=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}$$