x^2-1-x eching

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

Omil

$$\left(x-\frac{1-\sqrt{5}}{2}\right)\left(x-\frac{\sqrt{5}+1}{2}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

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

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.

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

-4 ni -1 marotabaga ko'paytirish.

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

1 ni 4 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{5}}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{5}}{2}$$

x=\frac{1±\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{5} ga qo'shish.

$$x=\frac{\sqrt{5}+1}{2}$$

x=\frac{1±\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{5} ni ayirish.

$$x=\frac{1-\sqrt{5}}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1+\sqrt{5}}{2} ga va x_{2} uchun \frac{1-\sqrt{5}}{2} ga bo‘ling.

$$x^{2}-x-1=\left(x-\frac{\sqrt{5}+1}{2}\right)\left(x-\frac{1-\sqrt{5}}{2}\right)$$

Baholash

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