4x-2-x^2/x-1=2x-4/x-1 eching

$$\frac { 4 x - 2 - x ^ { 2 } } { x - 1 } = \frac { 2 x - 4 } { x - 1 }$$

x uchun yechish

$$x=\sqrt{3}+1\approx 2,732050808$$

$$x=1-\sqrt{3}\approx -0,732050808$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$4x-2-x^{2}=2x-4$$

Ikkala tarafdan 2x ni ayirish.

$$4x-2-x^{2}-2x=-4$$

2x ni olish uchun 4x va -2x ni birlashtirish.

$$2x-2-x^{2}=-4$$

4 ni ikki tarafga qo’shing.

$$2x-2-x^{2}+4=0$$

2 olish uchun -2 va 4'ni qo'shing.

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

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

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

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 2 ni c bilan almashtiring.

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

2 kvadratini chiqarish.

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

-4 ni -1 marotabaga ko'paytirish.

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

4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+8}}{2\left(-1\right)}$$

4 ni 8 ga qo'shish.

$$x=\frac{-2±\sqrt{12}}{2\left(-1\right)}$$

12 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{3}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{3}}{-2}$$

x=\frac{-2±2\sqrt{3}}{-2} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{3} ga qo'shish.

$$x=\frac{2\sqrt{3}-2}{-2}$$

-2+2\sqrt{3} ni -2 ga bo'lish.

$$x=1-\sqrt{3}$$

x=\frac{-2±2\sqrt{3}}{-2} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{3} ni ayirish.

$$x=\frac{-2\sqrt{3}-2}{-2}$$

-2-2\sqrt{3} ni -2 ga bo'lish.

$$x=\sqrt{3}+1$$

Tenglama yechildi.

$$x=1-\sqrt{3} x=\sqrt{3}+1$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$4x-2-x^{2}=2x-4$$

Ikkala tarafdan 2x ni ayirish.

$$4x-2-x^{2}-2x=-4$$

2x ni olish uchun 4x va -2x ni birlashtirish.

$$2x-2-x^{2}=-4$$

2 ni ikki tarafga qo’shing.

$$2x-x^{2}=-4+2$$

-2 olish uchun -4 va 2'ni qo'shing.

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Ikki tarafini -1 ga bo‘ling.

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

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

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

2 ni -1 ga bo'lish.

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

-2 ni -1 ga bo'lish.

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

-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.

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

2 ni 1 ga qo'shish.

$$x^{2}-2x+1=3$$

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.

$$\left(x-1\right)^{2}=3$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{3}$$

Qisqartirish.

$$x-1=\sqrt{3} x-1=-\sqrt{3}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{3}+1 x=1-\sqrt{3}$$