x^2-2x+3=pi eching

$${ x }^{ 2 } -2x+3= \pi$$

x uchun yechish

$$x=\sqrt{\pi -2}+1\approx 2,068453393$$

$$x=-\sqrt{\pi -2}+1\approx -0,068453393$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-2x+3=\pi$$

Tenglamaning ikkala tarafidan \pi ni ayirish.

$$x^{2}-2x+3-\pi =\pi -\pi$$

O‘zidan \pi ayirilsa 0 qoladi.

$$x^{2}-2x+3-\pi =0$$

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 3-\pi ni c bilan almashtiring.

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

-2 kvadratini chiqarish.

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

-4 ni 3-\pi marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\pi -12}}{2}$$

4 ni -12+4\pi ga qo'shish.

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

-8+4\pi ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{\pi -2}}{2}$$

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

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

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

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

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

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

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}-2x+3=\pi$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x^{2}-2x+3-3=\pi -3$$

O‘zidan 3 ayirilsa 0 qoladi.

$$x^{2}-2x=\pi -3$$

-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.

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

\pi -3 ni 1 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

1 ni tenglamaning ikkala tarafiga qo'shish.

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