alpha^2+beta^2=(alpha+beta)^2-2 eching

$$\alpha ^ { 2 } + \beta ^ { 2 } = ( \alpha + \beta ) ^ { 2 } - 2$$

α uchun yechish

$$\alpha =\frac{1}{\beta }$$

$$\beta \neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\alpha +\beta \right)^{2} kengaytirilishi uchun ishlating.

$$\alpha ^{2}+\beta ^{2}=\alpha ^{2}+2\alpha \beta +\beta ^{2}-2$$

Ikkala tarafdan \alpha ^{2} ni ayirish.

$$\alpha ^{2}+\beta ^{2}-\alpha ^{2}=2\alpha \beta +\beta ^{2}-2$$

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

$$\beta ^{2}=2\alpha \beta +\beta ^{2}-2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2\alpha \beta +\beta ^{2}-2=\beta ^{2}$$

Ikkala tarafdan \beta ^{2} ni ayirish.

$$2\alpha \beta -2=\beta ^{2}-\beta ^{2}$$

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

$$2\alpha \beta -2=0$$

2 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2\alpha \beta =2$$

Tenglama standart shaklda.

$$2\beta \alpha =2$$

Ikki tarafini 2\beta ga bo‘ling.

$$\frac{2\beta \alpha }{2\beta }=\frac{2}{2\beta }$$

2\beta ga bo'lish 2\beta ga ko'paytirishni bekor qiladi.

$$\alpha =\frac{2}{2\beta }$$

2 ni 2\beta ga bo'lish.

$$\alpha =\frac{1}{\beta }$$

β uchun yechish

$$\beta =\frac{1}{\alpha }$$

$$\alpha \neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(\alpha +\beta \right)^{2} kengaytirilishi uchun ishlating.

$$\alpha ^{2}+\beta ^{2}=\alpha ^{2}+2\alpha \beta +\beta ^{2}-2$$

Ikkala tarafdan 2\alpha \beta ni ayirish.

$$\alpha ^{2}+\beta ^{2}-2\alpha \beta =\alpha ^{2}+\beta ^{2}-2$$

Ikkala tarafdan \beta ^{2} ni ayirish.

$$\alpha ^{2}+\beta ^{2}-2\alpha \beta -\beta ^{2}=\alpha ^{2}-2$$

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

$$\alpha ^{2}-2\alpha \beta =\alpha ^{2}-2$$

Ikkala tarafdan \alpha ^{2} ni ayirish.

$$-2\alpha \beta =\alpha ^{2}-2-\alpha ^{2}$$

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

$$-2\alpha \beta =-2$$

Tenglama standart shaklda.

$$\left(-2\alpha \right)\beta =-2$$

Ikki tarafini -2\alpha ga bo‘ling.

$$\frac{\left(-2\alpha \right)\beta }{-2\alpha }=-\frac{2}{-2\alpha }$$

-2\alpha ga bo'lish -2\alpha ga ko'paytirishni bekor qiladi.

$$\beta =-\frac{2}{-2\alpha }$$

-2 ni -2\alpha ga bo'lish.

$$\beta =\frac{1}{\alpha }$$