sqrt{x}=x/9 eching

$$\sqrt{ x } = \frac{ x }{ 9 }$$

x uchun yechish

$$x=0$$

$$x=81$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x}\right)^{2}=\left(\frac{x}{9}\right)^{2}$$

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

$$x=\left(\frac{x}{9}\right)^{2}$$

\frac{x}{9}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$x=\frac{x^{2}}{9^{2}}$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$x=\frac{x^{2}}{81}$$

Ikkala tarafdan \frac{x^{2}}{81} ni ayirish.

$$x-\frac{x^{2}}{81}=0$$

Tenglamaning ikkala tarafini 81 ga ko'paytirish.

$$81x-x^{2}=0$$

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.

$$-x^{2}+81x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 81 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-81±\sqrt{81^{2}}}{2\left(-1\right)}$$

81^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-81±81}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-81±81}{-2}$$

x=\frac{-81±81}{-2} tenglamasini yeching, bunda ± musbat. -81 ni 81 ga qo'shish.

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

0 ni -2 ga bo'lish.

$$x=0$$

x=\frac{-81±81}{-2} tenglamasini yeching, bunda ± manfiy. -81 dan 81 ni ayirish.

$$x=-\frac{162}{-2}$$

-162 ni -2 ga bo'lish.

$$x=81$$

Tenglama yechildi.

$$x=0 x=81$$

\sqrt{x}=\frac{x}{9} tenglamasida x uchun 0 ni almashtiring.

$$\sqrt{0}=\frac{0}{9}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{x}=\frac{x}{9} tenglamasida x uchun 81 ni almashtiring.

$$\sqrt{81}=\frac{81}{9}$$

Qisqartirish. x=81 tenglamani qoniqtiradi.

$$9=9$$

\sqrt{x}=\frac{x}{9} boʻyicha barcha yechimlar roʻyxati.

$$x=0 x=81$$