sqrt{98}:(x+4)(2x-3)=6 eching

$$\sqrt { 98 } : ( x + 4 ) ( 2 x - 3 ) = 6$$

x uchun yechish

$$x=\frac{231\sqrt{2}}{178}+\frac{183}{89}\approx 3,891479398$$

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.

$$\sqrt{98}\left(2x-3\right)=6\left(x+4\right)$$

Faktor: 98=7^{2}\times 2. \sqrt{7^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{7^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 7^{2} ning kvadrat ildizini chiqarish.

$$7\sqrt{2}\left(2x-3\right)=6\left(x+4\right)$$

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

$$14x\sqrt{2}-21\sqrt{2}=6\left(x+4\right)$$

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

$$14x\sqrt{2}-21\sqrt{2}=6x+24$$

Ikkala tarafdan 6x ni ayirish.

$$14x\sqrt{2}-21\sqrt{2}-6x=24$$

21\sqrt{2} ni ikki tarafga qo’shing.

$$14x\sqrt{2}-6x=24+21\sqrt{2}$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(14\sqrt{2}-6\right)x=24+21\sqrt{2}$$

Tenglama standart shaklda.

$$\left(14\sqrt{2}-6\right)x=21\sqrt{2}+24$$

Ikki tarafini 14\sqrt{2}-6 ga bo‘ling.

$$\frac{\left(14\sqrt{2}-6\right)x}{14\sqrt{2}-6}=\frac{21\sqrt{2}+24}{14\sqrt{2}-6}$$

14\sqrt{2}-6 ga bo'lish 14\sqrt{2}-6 ga ko'paytirishni bekor qiladi.

$$x=\frac{21\sqrt{2}+24}{14\sqrt{2}-6}$$

24+21\sqrt{2} ni 14\sqrt{2}-6 ga bo'lish.

$$x=\frac{231\sqrt{2}}{178}+\frac{183}{89}$$