left(1--1/2right)x^2+x+1-k=0 eching

$$\left( 1- \frac{ -1 }{ 2 } \right) { x }^{ 2 } +x+1-k = 0$$

k uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{-1}{2} kasri manfiy belgini olib tashlash bilan -\frac{1}{2} sifatida qayta yozilishi mumkin.

$$\left(1-\left(-\frac{1}{2}\right)\right)x^{2}+x+1-k=0$$

-\frac{1}{2} ning teskarisi \frac{1}{2} ga teng.

$$\left(1+\frac{1}{2}\right)x^{2}+x+1-k=0$$

\frac{3}{2} olish uchun 1 va \frac{1}{2}'ni qo'shing.

$$\frac{3}{2}x^{2}+x+1-k=0$$

Ikkala tarafdan \frac{3}{2}x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikkala tarafdan x ni ayirish.

$$1-k=-\frac{3}{2}x^{2}-x$$

Ikkala tarafdan 1 ni ayirish.

$$-k=-\frac{3}{2}x^{2}-x-1$$

Tenglama standart shaklda.

$$-k=-\frac{3x^{2}}{2}-x-1$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-k}{-1}=\frac{-\frac{3x^{2}}{2}-x-1}{-1}$$

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

$$k=\frac{-\frac{3x^{2}}{2}-x-1}{-1}$$

-\frac{3x^{2}}{2}-x-1 ni -1 ga bo'lish.

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

x uchun yechish (complex solution)

$$x=\frac{\sqrt{6k-5}-1}{3}$$

$$x=\frac{-\sqrt{6k-5}-1}{3}$$

x uchun yechish

$$x=\frac{\sqrt{6k-5}-1}{3}$$

$$x=\frac{-\sqrt{6k-5}-1}{3}\text{, }k\geq \frac{5}{6}$$