(a-x)^2+3^2=x^2 eching

$$( a - x ) ^ { 2 } + 3 ^ { 2 } = x ^ { 2 }$$

x uchun yechish

$$x=\frac{a}{2}+\frac{9}{2a}$$

$$a\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-x\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}-2ax+x^{2}+3^{2}=x^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$a^{2}-2ax+x^{2}+9=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$a^{2}-2ax+x^{2}+9-x^{2}=0$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$a^{2}-2ax+9=0$$

Ikkala tarafdan a^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-2ax+9=-a^{2}$$

Ikkala tarafdan 9 ni ayirish.

$$-2ax=-a^{2}-9$$

Tenglama standart shaklda.

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

Ikki tarafini -2a ga bo‘ling.

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

-2a ga bo'lish -2a ga ko'paytirishni bekor qiladi.

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

-a^{2}-9 ni -2a ga bo'lish.

$$x=\frac{a}{2}+\frac{9}{2a}$$

a uchun yechish (complex solution)

$$a=-\sqrt{x^{2}-9}+x$$

$$a=\sqrt{x^{2}-9}+x$$

a uchun yechish

$$a=-\sqrt{x^{2}-9}+x$$

$$a=\sqrt{x^{2}-9}+x\text{, }|x|\geq 3$$