(z^2+z)+(z^2-11) eching

$$( { z }^{ 2 } +z)+( { z }^{ 2 } -11)$$

Omil

$$2\left(z-\frac{-\sqrt{89}-1}{4}\right)\left(z-\frac{\sqrt{89}-1}{4}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

2z^{2} ni olish uchun z^{2} va z^{2} ni birlashtirish.

$$factor(2z^{2}+z-11)$$

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.

$$2z^{2}+z-11=0$$

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.

$$z=\frac{-1±\sqrt{1^{2}-4\times 2\left(-11\right)}}{2\times 2}$$

1 kvadratini chiqarish.

$$z=\frac{-1±\sqrt{1-4\times 2\left(-11\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$z=\frac{-1±\sqrt{1-8\left(-11\right)}}{2\times 2}$$

-8 ni -11 marotabaga ko'paytirish.

$$z=\frac{-1±\sqrt{1+88}}{2\times 2}$$

1 ni 88 ga qo'shish.

$$z=\frac{-1±\sqrt{89}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$z=\frac{-1±\sqrt{89}}{4}$$

z=\frac{-1±\sqrt{89}}{4} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{89} ga qo'shish.

$$z=\frac{\sqrt{89}-1}{4}$$

z=\frac{-1±\sqrt{89}}{4} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{89} ni ayirish.

$$z=\frac{-\sqrt{89}-1}{4}$$

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{89}}{4} ga va x_{2} uchun \frac{-1-\sqrt{89}}{4} ga bo‘ling.

$$2z^{2}+z-11=2\left(z-\frac{\sqrt{89}-1}{4}\right)\left(z-\frac{-\sqrt{89}-1}{4}\right)$$

Baholash

$$2z^{2}+z-11$$

Yechim qadamlari

2z^{2} ni olish uchun z^{2} va z^{2} ni birlashtirish.

$$2z^{2}+z-11$$