sqrt{x}=xdiv2 eching

$$\sqrt{ x } = x \div 2$$

x uchun yechish

$$x=0$$

$$x=4$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x}\right)^{2}=\left(\frac{x}{2}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x} ga hisoblang va x ni qiymatni oling.

$$x=\left(\frac{x}{2}\right)^{2}$$

\frac{x}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$x=\frac{x^{2}}{2^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x=\frac{x^{2}}{4}$$

Ikkala tarafdan \frac{x^{2}}{4} ni ayirish.

$$x-\frac{x^{2}}{4}=0$$

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

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

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 4 ni b va 0 ni c bilan almashtiring.

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

4^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±4}{-2}$$

x=\frac{-4±4}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 4 ga qo'shish.

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

x=\frac{-4±4}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 4 ni ayirish.

$$x=-\frac{8}{-2}$$

-8 ni -2 ga bo'lish.

$$x=4$$

Tenglama yechildi.

$$x=0 x=4$$

\sqrt{x}=\frac{x}{2} tenglamasida x uchun 0 ni almashtiring.

$$\sqrt{0}=\frac{0}{2}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{x}=\frac{x}{2} tenglamasida x uchun 4 ni almashtiring.

$$\sqrt{4}=\frac{4}{2}$$

Qisqartirish. x=4 tenglamani qoniqtiradi.

$$2=2$$

\sqrt{x}=\frac{x}{2} boʻyicha barcha yechimlar roʻyxati.

$$x=0 x=4$$