x=x+1/x-1 eching

$$x = \frac { x + 1 } { x - 1 }$$

x uchun yechish

$$x=\sqrt{2}+1\approx 2,414213562$$

$$x=1-\sqrt{2}\approx -0,414213562$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{x+1}{x-1} ni ayirish.

$$x-\frac{x+1}{x-1}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{x\left(x-1\right)}{x-1}-\frac{x+1}{x-1}=0$$

\frac{x\left(x-1\right)}{x-1} va \frac{x+1}{x-1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(x-1\right)-\left(x+1\right)}{x-1}=0$$

x\left(x-1\right)-\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-x-x-1}{x-1}=0$$

x^{2}-x-x-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-2x-1}{x-1}=0$$

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-1 ga ko'paytirish.

$$x^{2}-2x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4}}{2}$$

4 ni 4 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{2}}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{2}}{2}$$

x=\frac{2±2\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{2} ga qo'shish.

$$x=\frac{2\sqrt{2}+2}{2}$$

2+2\sqrt{2} ni 2 ga bo'lish.

$$x=\sqrt{2}+1$$

x=\frac{2±2\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{2} ni ayirish.

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

2-2\sqrt{2} ni 2 ga bo'lish.

$$x=1-\sqrt{2}$$

Tenglama yechildi.

$$x=\sqrt{2}+1 x=1-\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan \frac{x+1}{x-1} ni ayirish.

$$x-\frac{x+1}{x-1}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{x\left(x-1\right)}{x-1}-\frac{x+1}{x-1}=0$$

\frac{x\left(x-1\right)}{x-1} va \frac{x+1}{x-1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(x-1\right)-\left(x+1\right)}{x-1}=0$$

x\left(x-1\right)-\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-x-x-1}{x-1}=0$$

x^{2}-x-x-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-2x-1}{x-1}=0$$

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-1 ga ko'paytirish.

$$x^{2}-2x-1=0$$

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}-2x=1$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=1+1$$

1 ni 1 ga qo'shish.

$$x^{2}-2x+1=2$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=2$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{2}$$

Qisqartirish.

$$x-1=\sqrt{2} x-1=-\sqrt{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{2}+1 x=1-\sqrt{2}$$