x^2-x*2x+1-x^2=2x^2+4x-x-1 eching

$${ x }^{ 2 } -x \times 2x+1- { x }^{ 2 } =2 { x }^{ 2 } +4x-x-1$$

x uchun yechish

$$x=\frac{\sqrt{41}-3}{8}\approx 0,42539053$$

$$x=\frac{-\sqrt{41}-3}{8}\approx -1,17539053$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}-x^{2}\times 2+1-x^{2}=2x^{2}+4x-x-1$$

-x^{2} ni olish uchun x^{2} va -x^{2}\times 2 ni birlashtirish.

$$-x^{2}+1-x^{2}=2x^{2}+4x-x-1$$

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$-2x^{2}+1=2x^{2}+4x-x-1$$

3x ni olish uchun 4x va -x ni birlashtirish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

-4x^{2} ni olish uchun -2x^{2} va -2x^{2} ni birlashtirish.

$$-4x^{2}+1=3x-1$$

Ikkala tarafdan 3x ni ayirish.

$$-4x^{2}+1-3x=-1$$

1 ni ikki tarafga qo’shing.

$$-4x^{2}+1-3x+1=0$$

2 olish uchun 1 va 1'ni qo'shing.

$$-4x^{2}+2-3x=0$$

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.

$$-4x^{2}-3x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -4 ni a, -3 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-4\right)\times 2}}{2\left(-4\right)}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-4\right)\times 2}}{2\left(-4\right)}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+16\times 2}}{2\left(-4\right)}$$

16 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+32}}{2\left(-4\right)}$$

9 ni 32 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{41}}{2\left(-4\right)}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{41}}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{3±\sqrt{41}}{-8}$$

x=\frac{3±\sqrt{41}}{-8} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{41} ga qo'shish.

$$x=\frac{\sqrt{41}+3}{-8}$$

3+\sqrt{41} ni -8 ga bo'lish.

$$x=\frac{-\sqrt{41}-3}{8}$$

x=\frac{3±\sqrt{41}}{-8} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{41} ni ayirish.

$$x=\frac{3-\sqrt{41}}{-8}$$

3-\sqrt{41} ni -8 ga bo'lish.

$$x=\frac{\sqrt{41}-3}{8}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{41}-3}{8} x=\frac{\sqrt{41}-3}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}-x^{2}\times 2+1-x^{2}=2x^{2}+4x-x-1$$

-x^{2} ni olish uchun x^{2} va -x^{2}\times 2 ni birlashtirish.

$$-x^{2}+1-x^{2}=2x^{2}+4x-x-1$$

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$-2x^{2}+1=2x^{2}+4x-x-1$$

3x ni olish uchun 4x va -x ni birlashtirish.

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

Ikkala tarafdan 2x^{2} ni ayirish.

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

-4x^{2} ni olish uchun -2x^{2} va -2x^{2} ni birlashtirish.

$$-4x^{2}+1=3x-1$$

Ikkala tarafdan 3x ni ayirish.

$$-4x^{2}+1-3x=-1$$

Ikkala tarafdan 1 ni ayirish.

$$-4x^{2}-3x=-1-1$$

-2 olish uchun -1 dan 1 ni ayirish.

$$-4x^{2}-3x=-2$$

Ikki tarafini -4 ga bo‘ling.

$$\frac{-4x^{2}-3x}{-4}=-\frac{2}{-4}$$

-4 ga bo'lish -4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{3}{-4}\right)x=-\frac{2}{-4}$$

-3 ni -4 ga bo'lish.

$$x^{2}+\frac{3}{4}x=-\frac{2}{-4}$$

\frac{-2}{-4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{3}{4}x=\frac{1}{2}$$

\frac{3}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{8} olish uchun. Keyin, \frac{3}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{4}x+\left(\frac{3}{8}\right)^{2}=\frac{1}{2}+\left(\frac{3}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{8} kvadratini chiqarish.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=\frac{1}{2}+\frac{9}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni \frac{9}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=\frac{41}{64}$$

x^{2}+\frac{3}{4}x+\frac{9}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{8}\right)^{2}=\frac{41}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{8}\right)^{2}}=\sqrt{\frac{41}{64}}$$

Qisqartirish.

$$x+\frac{3}{8}=\frac{\sqrt{41}}{8} x+\frac{3}{8}=-\frac{\sqrt{41}}{8}$$

Tenglamaning ikkala tarafidan \frac{3}{8} ni ayirish.

$$x=\frac{\sqrt{41}-3}{8} x=\frac{-\sqrt{41}-3}{8}$$