(x-2-sqrt{3})(x-2+sqrt{3})=? eching

$$( x - 2 - \sqrt { 3 } ) ( x - 2 + \sqrt { 3 } ) = ?$$

Baholash

$$x^{2}-4x+1$$

Yechim qadamlari

x-2-\sqrt{3} ifodaning har bir elementini x-2+\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$x^{2}-2x+x\sqrt{3}-2x+4-2\sqrt{3}-\sqrt{3}x+2\sqrt{3}-\left(\sqrt{3}\right)^{2}$$

-4x ni olish uchun -2x va -2x ni birlashtirish.

$$x^{2}-4x+x\sqrt{3}+4-2\sqrt{3}-\sqrt{3}x+2\sqrt{3}-\left(\sqrt{3}\right)^{2}$$

0 ni olish uchun x\sqrt{3} va -\sqrt{3}x ni birlashtirish.

$$x^{2}-4x+4-2\sqrt{3}+2\sqrt{3}-\left(\sqrt{3}\right)^{2}$$

0 ni olish uchun -2\sqrt{3} va 2\sqrt{3} ni birlashtirish.

$$x^{2}-4x+4-\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$x^{2}-4x+4-3$$

1 olish uchun 4 dan 3 ni ayirish.

$$x^{2}-4x+1$$

x ga nisbatan hosilani topish

$$2\left(x-2\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

x-2-\sqrt{3} ifodaning har bir elementini x-2+\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x+x\sqrt{3}-2x+4-2\sqrt{3}-\sqrt{3}x+2\sqrt{3}-\left(\sqrt{3}\right)^{2})$$

-4x ni olish uchun -2x va -2x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x+x\sqrt{3}+4-2\sqrt{3}-\sqrt{3}x+2\sqrt{3}-\left(\sqrt{3}\right)^{2})$$

0 ni olish uchun x\sqrt{3} va -\sqrt{3}x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x+4-2\sqrt{3}+2\sqrt{3}-\left(\sqrt{3}\right)^{2})$$

0 ni olish uchun -2\sqrt{3} va 2\sqrt{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x+4-\left(\sqrt{3}\right)^{2})$$

\sqrt{3} kvadrati – 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x+4-3)$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x+1)$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

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

2 dan 1 ni ayirish.

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

1 dan 1 ni ayirish.

$$2x^{1}-4x^{0}$$

Har qanday t sharti uchun t^{1}=t.

$$2x-4x^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$2x-4$$