sqrt[8]{8}:(x+4)(2x-3)=6 eching

$$\sqrt[ 8 ] { 8 } : ( x + 4 ) ( 2 x - 3 ) = 6$$

x uchun yechish

$$x = -\frac{3 \cdot 2 ^ {\frac{3}{8}} {(2 \sqrt{2} + 81)} {(4 \cdot 2 ^ {\frac{5}{8}} + 1)} {(2 ^ {\frac{3}{8}} + 3)} {(2 ^ {\frac{3}{4}} + 9)}}{13106} \approx -8,187871771$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+4 ga ko'paytirish.

$$\sqrt[8]{8}\left(2x-3\right)=6\left(x+4\right)$$

\sqrt[8]{8} ga 2x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}=6\left(x+4\right)$$

6 ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}=6x+24$$

Ikkala tarafdan 6x ni ayirish.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}-6x=24$$

3\sqrt[8]{8} ni ikki tarafga qo’shing.

$$2\sqrt[8]{8}x-6x=24+3\sqrt[8]{8}$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2\sqrt[8]{8}-6\right)x=24+3\sqrt[8]{8}$$

Tenglama standart shaklda.

$$\left(2\sqrt[8]{8}-6\right)x=3\sqrt[8]{8}+24$$

Ikki tarafini 2\sqrt[8]{8}-6 ga bo‘ling.

$$\frac{\left(2\sqrt[8]{8}-6\right)x}{2\sqrt[8]{8}-6}=\frac{3\times 2^{\frac{3}{8}}+24}{2\sqrt[8]{8}-6}$$

2\sqrt[8]{8}-6 ga bo'lish 2\sqrt[8]{8}-6 ga ko'paytirishni bekor qiladi.

$$x=\frac{3\times 2^{\frac{3}{8}}+24}{2\sqrt[8]{8}-6}$$

24+3\times 2^{\frac{3}{8}} ni 2\sqrt[8]{8}-6 ga bo'lish.

$$x=-\frac{3\left(2\sqrt{2}+81\right)\left(2^{\frac{3}{8}}+3\right)\left(2^{\frac{3}{4}}+9\right)\left(2^{\frac{7}{8}}+1\right)\sqrt[8]{2}\left(\sqrt[4]{2}+4-2\sqrt[8]{2}\right)}{13106}$$