4a^2-4a-1= eching

$$4 a ^ { 2 } - 4 a - 1 =$$

Omil

$$4\left(a-\frac{1-\sqrt{2}}{2}\right)\left(a-\frac{\sqrt{2}+1}{2}\right)$$

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.

$$4a^{2}-4a-1=0$$

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.

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

-4 kvadratini chiqarish.

$$a=\frac{-\left(-4\right)±\sqrt{16-4\times 4\left(-1\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$a=\frac{-\left(-4\right)±\sqrt{16-16\left(-1\right)}}{2\times 4}$$

-16 ni -1 marotabaga ko'paytirish.

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

16 ni 16 ga qo'shish.

$$a=\frac{-\left(-4\right)±\sqrt{32}}{2\times 4}$$

32 ning kvadrat ildizini chiqarish.

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

-4 ning teskarisi 4 ga teng.

$$a=\frac{4±4\sqrt{2}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$a=\frac{4±4\sqrt{2}}{8}$$

a=\frac{4±4\sqrt{2}}{8} tenglamasini yeching, bunda ± musbat. 4 ni 4\sqrt{2} ga qo'shish.

$$a=\frac{4\sqrt{2}+4}{8}$$

4+4\sqrt{2} ni 8 ga bo'lish.

$$a=\frac{\sqrt{2}+1}{2}$$

a=\frac{4±4\sqrt{2}}{8} tenglamasini yeching, bunda ± manfiy. 4 dan 4\sqrt{2} ni ayirish.

$$a=\frac{4-4\sqrt{2}}{8}$$

4-4\sqrt{2} ni 8 ga bo'lish.

$$a=\frac{1-\sqrt{2}}{2}$$

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{2}}{2} ga va x_{2} uchun \frac{1-\sqrt{2}}{2} ga bo‘ling.

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

Baholash

$$4a^{2}-4a-1$$