y^2-6y+7 eching

$${ y }^{ 2 } -6y+7$$

Omil

$$\left(y-\left(3-\sqrt{2}\right)\right)\left(y-\left(\sqrt{2}+3\right)\right)$$

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.

$$y^{2}-6y+7=0$$

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.

$$y=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 7}}{2}$$

-6 kvadratini chiqarish.

$$y=\frac{-\left(-6\right)±\sqrt{36-4\times 7}}{2}$$

-4 ni 7 marotabaga ko'paytirish.

$$y=\frac{-\left(-6\right)±\sqrt{36-28}}{2}$$

36 ni -28 ga qo'shish.

$$y=\frac{-\left(-6\right)±\sqrt{8}}{2}$$

8 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-6\right)±2\sqrt{2}}{2}$$

-6 ning teskarisi 6 ga teng.

$$y=\frac{6±2\sqrt{2}}{2}$$

y=\frac{6±2\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{2} ga qo'shish.

$$y=\frac{2\sqrt{2}+6}{2}$$

6+2\sqrt{2} ni 2 ga bo'lish.

$$y=\sqrt{2}+3$$

y=\frac{6±2\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{2} ni ayirish.

$$y=\frac{6-2\sqrt{2}}{2}$$

6-2\sqrt{2} ni 2 ga bo'lish.

$$y=3-\sqrt{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 3+\sqrt{2} ga va x_{2} uchun 3-\sqrt{2} ga bo‘ling.

$$y^{2}-6y+7=\left(y-\left(\sqrt{2}+3\right)\right)\left(y-\left(3-\sqrt{2}\right)\right)$$

Baholash

$$y^{2}-6y+7$$