(7x-a)^2=49x^2-bx+9 eching

$$( 7 x - a ) ^ { 2 } = 49 x ^ { 2 } - b x + 9$$

b uchun yechish (complex solution)

$$\left\{\begin{matrix}b=\frac{14ax-a^{2}+9}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&\left(a=-3\text{ or }a=3\right)\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(7x-a\right)^{2} kengaytirilishi uchun ishlating.

$$49x^{2}-14xa+a^{2}=49x^{2}-bx+9$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$49x^{2}-bx+9=49x^{2}-14xa+a^{2}$$

Ikkala tarafdan 49x^{2} ni ayirish.

$$-bx+9=49x^{2}-14xa+a^{2}-49x^{2}$$

0 ni olish uchun 49x^{2} va -49x^{2} ni birlashtirish.

$$-bx+9=-14xa+a^{2}$$

Ikkala tarafdan 9 ni ayirish.

$$-bx=-14xa+a^{2}-9$$

Tenglama standart shaklda.

$$\left(-x\right)b=-14ax+a^{2}-9$$

Ikki tarafini -x ga bo‘ling.

$$\frac{\left(-x\right)b}{-x}=\frac{-14ax+a^{2}-9}{-x}$$

-x ga bo'lish -x ga ko'paytirishni bekor qiladi.

$$b=\frac{-14ax+a^{2}-9}{-x}$$

-14xa+a^{2}-9 ni -x ga bo'lish.

$$b=-\frac{-14ax+a^{2}-9}{x}$$

b uchun yechish

$$\left\{\begin{matrix}b=\frac{14ax-a^{2}+9}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }|a|=3\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(7x-a\right)^{2} kengaytirilishi uchun ishlating.

$$49x^{2}-14xa+a^{2}=49x^{2}-bx+9$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$49x^{2}-bx+9=49x^{2}-14xa+a^{2}$$

Ikkala tarafdan 49x^{2} ni ayirish.

$$-bx+9=49x^{2}-14xa+a^{2}-49x^{2}$$

0 ni olish uchun 49x^{2} va -49x^{2} ni birlashtirish.

$$-bx+9=-14xa+a^{2}$$

Ikkala tarafdan 9 ni ayirish.

$$-bx=-14xa+a^{2}-9$$

Tenglama standart shaklda.

$$\left(-x\right)b=-14ax+a^{2}-9$$

Ikki tarafini -x ga bo‘ling.

$$\frac{\left(-x\right)b}{-x}=\frac{-14ax+a^{2}-9}{-x}$$

-x ga bo'lish -x ga ko'paytirishni bekor qiladi.

$$b=\frac{-14ax+a^{2}-9}{-x}$$

-14xa+a^{2}-9 ni -x ga bo'lish.

$$b=-\frac{-14ax+a^{2}-9}{x}$$

a uchun yechish (complex solution)

$$a=\sqrt{49x^{2}-bx+9}+7x$$

$$a=-\sqrt{49x^{2}-bx+9}+7x$$